TL;DR: Arena Express Mode can offer between 6% and 15% speed increases in the arena, depending on how you grind arena and what precisely constitutes a "speed increase."
With all the discussion surrounding Arena Express Mode (some of it even predating the actual release of the feature) I wanted to take a close look at the actual quantitative benefit of using the mode, to put the feature into context. it is described (by Kabam) as a QoL arena feature, is it?
Let's start by what the Arena Express Feature does.

Express mode is enabled with a checkbox from within the arena (and yes, this is pretty much the worst possible place to put this). When this checkbox is selected, picking Quick Fill and then starting a match will skip the match selection screen:

and jump straight to the easy match. You do still have an opportunity to rearrange champions within the match, When the fight is completed, the arena advances to the next fight, then the next one, and then finally back to the team selection screen. This streamlines an arena match by removing a few screens, but how much time savings is this?
Well, it depends. Many of the screens being skipped could also be advanced through by tapping, so the amount of time saved depends on how fast and aggressive the player is. Also, since one of the screens skipped is the match selection screen, how much time is saved depends on how long a player used to linger on that screen and think about picking the next match. In very informal testing, I measured the amount of time saved per match to be on the order of fifteen to twenty seconds total, which at about two minutes per round would be about 15% improvement in speed.
However, the situation is more complex than that, for reasons that will require a detour. The benefit of arena express actually depends on how you grind the arena, and what your arena goal is. This may not seem obvious, so let's discuss this in broad strokes. Suppose my goal every arena iteration is to get all of the milestones in the featured arena. To do this I run all my 6* champs through the arena, as many times as it takes to reach 12 million points and then stop. Arena express mode will help me, but in a very specific way: it will help me by allowing me to do this in less time. It will not increase the amount of points I can earn, because I'm already reaching my point goal as it is. I'm faster, but I earn no more points and gain no more rewards. The benefit is purely a matter of this process taking less time.
However, if I am attempting to grind for the 6* featured champ, say, then arena express should not just speed me up, it should also increase the total amount of points I can earn, specifically because I am going faster, and will likely spend the same amount of time to try to get as much points as possible. Here, the benefit is not spending less time, it is earning more points.
Okay, but that's just a minor quibble, right? Whether we reach a certain point goal faster or get more points spending the same amount of time, that's just two different ways to describe the same benefit, right? Well it would be, if it wasn't for the fact that these two players are also probably not grinding in the same way. This gets back to
how arena express delivers its benefits. It skips screens players would ordinarily spend more time on, and it immediately picks a match and runs with it rather than waiting for the player to pick one. And it is the easy match.
For a casual grinder, these two choices are overall a net benefit. Casual grinders probably linger on screens longer than necessary, they often do not have 100% of their attention focused on the arena. And while picking the easy match isn't always the optimal choice, for casual grinders it is generally good enough. These people will probably see the ~15% reduction in time spent I mentioned above. But a
competitive grinder, or someone that is focusing more of their attention and time to get more points in the arena isn't, because they will get less time savings from skipped screens and might also potential lose points from consistently running the easy match choice (it scores fewer points). So I decided to test this carefully.
I ran a long sequence of matches in both the featured and basic arena, running 6* champs in the featured and 5* champs in the basic. I ran long enough match sequences to allow random match circumstances to average out. And I also ran the arenas as fast as I could, to compare arena express mode to non-express mode for a player who wasn't wasting as much time on the accelerated parts of arena.
With arena express mode on, I was able to do 36 rounds in the basic arena in 79 minutes (no recoil masteries) scoring 3,112,959 points. This is 27.3 round per hour, 2,364,272 points per hour. In the featured arena I was able to do 70 rounds in 151.5 minutes scoring 14,784,309 points. That is 27.7 rounds per hour and 5,855,172 points per hour.
I then did the featured arena again with the same roster fully recharged, but with arena express mode off. This time 70 rounds took 165 minutes scoring 14,804,241 points. This is 25.4 rounds per hour and 5,389,894 points per hour. Compared to non-arena express mode, arena express mode was allowing me to do arena rounds 9% faster and generate points 8.6% faster. This is less improvement than the "casual" numbers would imply, because I am speeding through the screens that arena express mode eliminates, and because I am spending as close to zero time thinking about the match selections as possible. Since I am attempting to replicate what arena express is doing, I am simply mindlessly picking the easy match every time, which reduces the speed benefit of skipping the selection screen. It also makes sense that the match acceleration and point acceleration would be essentially the same, as I am basically replicating the same scoring environment.
For the basic arena, I redid my express run with arena express off, but instead of picking the easy match every time I picked the hard one every time. In prior testing I found that while picking the harder match *can* generate more points, it is tricky because when you're casually grinding you're more likely to lose a match against the harder match selection. This can erode the point benefit to the point of making it counterproductive in many cases. However, for this test I was not casually grinding and focused on winning every fight as quickly as possible. In this run I did 36 rounds in 88 minutes scoring 3,264,275 points. This resulted in a net rate of 24.5 rounds per hour and 2,225,710 points per hour. This compared to these numbers, arena express mode was 11% faster in terms of arena rounds per hour, but only 6% faster in terms of points per hour.
So the overall benefit of arena express seems to depend on how you grind, and I haven't explicitly tested many other corner cases, such as repeatedly refreshing the same champions as part of a featured run. However, it is clear that the overall benefit covers a pretty wide range. The most casual grinders who are naturally slow in general can see speed ups of as much as 15% or more. Fast grinders that are already scoring lots of points and doing lots of rounds might see benefits as low as 6% or possibly less. It does seem to be the case that the slower you are and the less points you typically grind out, the more benefit you will get from express mode. Meanwhile the faster you are at running through the arena mode and the more points you strive to score, the less benefit you will get, although you will still get some benefit.
One other thing worth addressing. Is arena express a "QoL" feature? Well, it is and it isn't. In strict literal terms, arena express accelerates earning rewards in the arena. That makes it not a "pure" QoL benefit. It is in effect a reward enhancement. However, it
delivers that benefit in a classically QoL way: by streamlining the UI of the mode. Streamlining UI is typically the realm of QoL. It is the grinding nature of the arena that creates this unusual overlap between the streamlining of the interface and the resultant rewards that is somewhat unique. I would say arena express is a QoL feature that has non-QoL benefits, and is neither a 100% QoL feature nor 100% not a QoL feature.
Last thing: recoil masteries have a huge impact on arena speed. Putting those back on for me would swamp all of these benefits by a significant margin. If you're concerned about Sigil players having a substantial advantage in the arena and you don't have recoil masteries on, everyone who does is already blowing your arena speed away by huge margins.