I think that in terms of raw aiming, gyro + analog can come up on top ahead of analog alone, but raw aiming is not what you're doing in most games. In games with aim assist, I find that the analog aim can be very accurate, and in those games gyro can actually interfere with your aim in a negative way.
Splatoon is a good example of where gyro + analog comes out on top, because there is no aim assist for analog players. So aiming with analog alone isn't all that easy, and gyro can help compensate some of the missing precision and enable you to flick onto targets more consistently.
But in my own experience, in games where the analog sticks already have aim assist applied, then gyro isn't helpful at all. My aim can already be strong without the gyro and the gyro adds an unsteadyness to my aim and tracking that I generally do not want. Yes, this scenario has been biased in favour of analog aiming because aim assist is present to help that style of aiming, without help provided to the others, but that's where we're at. Game developers reliably provide aim assist for their analog players and removing that would deter more players than it would bring in to include gyro, so a best case scenario is that you have gyro alongside assisted analog aiming, wherein gyro aiming and then gyro aiming doesn't stack up all that well.
For context, with aim assist, analog aiming is often more accurate than even mouse aiming. In games like Destiny and Apex Legends you have people competing using controllers at the highest level of play, and many top PC players complaining that controllers are too accurate when compared to keyboard and mouse usage.
As is, I can load up Apex Legends on PC with a controller and fry just about anyone. It doesn't feel like a disadvantage using a controller, in fact I've wrote about this before but PC lobbies actually feel easier than console lobbies, with the range of skill being wider (some people really, really suck on keyboard and mouse).
Yes, again you could say get rid of the aim assist then, but there are millions of players who have invested in analog aiming and find that an easy way to play their shooters. On cross platform games like Call of Duty and Apex Legends, you have more people using analog aiming than any other input method available, so removing aim assist would likely spoil the game for the majority audience.
The other issue is that combined gyro + analog (Splatoon style) aiming is arguably the least accessible of the three options. It requires you to learn a dual analog aiming system, and on top of that, manage the gyro at the same time. I initial barrier to entry is high for gyro + analog, and the ongoing learning curve is steeper. This perhaps isn't true where dual analog is a less good option, for instance on Switch where the analog sticks are small and unweildy, I think gyro aiming is better and easier to adapt to because of how difficult the dual analog can be on the joycons.
So in sum, I think to really see the benefit of gyro you would need to remove dual analogues aim assist, which just isn't going to happen. As is, gyro + dual is just more work for a lot of players, and the pay off in most games isn't really there. I don't see why this scenario would change any time soon, so I don't see why we would expect mainstream adoption of gyro aiming.
The best path forward is to include gyro augmented aiming as an option in every game, and see how its audience grows. In the distant future it might displace analog aiming, but that would just create a bigger disparity between mouse and controller than we already have, so it's likely that gyro would need its own aim assist solution to hit the same peak. That then becomes a complex scenario, because if this more complex middle ground still needs assistance to see similar accuracy with mouse and key. That might raise a question as to why bother with gyro if it still needs assistance to hit mouse and key accuracy, but I think the answer is because options are good, particularly for accessibility.
Another factor to consider will be how gyro aiming interacts with haptics which is obviously a direction that Sony are really pushing into. I know on Killzone 3's motion control option the vibration made your accuracy and recoil control considerably worse, which is obviously a barrier to tackle. If the gyro were able to communicate with the haptics in some way, I imagine you could stabilise the input and keep vibration on, but I don't know if we'd ever see such a thing.
Aiming is literally what gyro is best at. Always on is not ideal though. Here's a joystick vs gyro / mouse test, where joystick is a pretty distant 3rd in performance:
People are always posting this video but there are a tonne of issues with it.
a) It offers only one persons experience of the three aiming styles. It's very possible they are better/worse than other people in certain areas, and honestly, very likely that this person is much more practiced with gyro than most people are. In any case, it's a single data point, not a representative sample.
b) The type of aiming isn't representative of the scenarios featured in most games or every game. Depending on the game the number of targets on screen are going to be between 1 and perhaps 4. The targets on screen are rarely going to be as small as even the larger targets in aim lab, and the targets and player are both moving. The scenario also presents targets across varying levels of elevation, whereas most games have enemies presented on the same level of elevation (flat ground), analog users really struggle with those diagonal adjustments, but less so with straight horizontal. Further, the scenario only focuses on initial target acquisition not long-term accuracy, recoil control and tracking.
c) This is a raw aim comparison, almost all shooters have aim assist for controller players and that's not going to disappear.