Let's establish something first, I am not here to justify the martial art to you, I can explain the system to you based off of my training and experience but that's it, there's no need and its not possible to "prove" a system on a message board on the internet.
MMA is heavily favored towards making accommodations for BJJ that are unrealistic and allow for more completed techniques. when you shoot for the double leg, the part of your head left open is the spine and the back of the head behind the ears, striking this area is called rabbit punching and it is 100% banned in the UFC and most MMA competitions, so its convenient that the move that will most efficiently counter the takedown is also banned in the same arena where it is "most successful". Is there a reason? Yes, MMA is a sport, the rules in MMA favor ensuring longevity for the fighters. Shoot for a double leg in a real altercation and watch how fast you get your bell rung, that's not theory or anecdote, that's experiential wisdom, do what you want with that on your own time.
Small joint manipulation is 100% not allowed in MMA, with this and the gloves, sweat, bare skin, petroleum jelly and other oilyness during an MMA fight it makes wristlocks impractical for all intents and purposes. There's a huge difference between you grabbing my jacket at the start of a confrontation and me attempting to wristlock you and us squaring off with MMA gloves and greased up at the start of a UFC fight. There's also a threshold for what I will and won't try in a fight with someone who is also a professional fighter, before you get too excited, this list also includes the double leg as something I would write off against a trained fighter.
The piledriver and any slam that could injure the head or back of an opponent is 100% not legal in the UFC, it just so happens that this is one of the more effective ways of countering someone attempting to pull you down for some BJJ, or attempting to grapple a standing opponent. Is there a good reason for it being banned? Yes. That doesn't change the fact that the RESULT, favors the BJJ practitioner.
Strikes to a downed or grounded opponents head are not allowed in the UFC, here's a disqualifying knee to the head:
https://twitter.com/btsportufc/status/1368517678420361229?ref_src=twsrc^tfw|twcamp^tweetembed|twterm^1368517678420361229|twgr^|twcon^s1_c10&ref_url=https://www.sportskeeda.com/mma/which-moves-illegal-ufc
IS there a reason for this? Yes, a good one, having to do with the longevity and safety of the fighters involved. Still, it's another example of a protection enjoyed by BJJ that falsely inflates the effectiveness of the system. BJJ is great at ground fighting, the problem is you don't want to be on the ground in a fight and when you "shoot" at an opponents waist, fight on your back, etc, your going to tend to catch a beating for exposing your self. The system isn't worthless, in fact there's an argument to be made that BJJ should be integrated into more systems so that you have the tools to escape a fight on the ground or to finish an altercation that goes there, albeit with some caveats. I could make the same claim for Aikido however in regards to how it is incomplete as a single style but able to wonderfully complement a more traditional striking system. You can't simply point at BJJ and say "this works" and then point to Aikido and say "this doesn't work" as blanket statements towards the whole system.
Your argument "we don't see guys escaping grabs with wrist locks" or that "other arts do the thing that they claim" is more false pretense. Aikido does what it claims to do as much as any other system. Those stupid wrist locks you say don't work are taught to the police and military because they do work, when correctly applied, despite what you or I may think about these classes overall, they are taught because they work, if they didn't we wouldn't have a hundred years of Aikido and Judo techniques being integrated into law enforcement and military training, it would have been opted out by now if it were so wildly ineffective. Add to that, many police departments mandate those techniques trained in their classes as the ONLY ones available to officers for liability purposes, if there was no merit to them, we would have seen an outcry of officers protesting their ineffectual training. Say what you want, but the average cop is going to see and participate in more violent altercations than most other citizens. More cops use these techniques than most martial artists ever get to use their martial arts in street fights.
There's nothing wrong with the tools in the system, they work, when properly applied. Conflating youtube videos as the final arbiter of what is real is stupid, by that standard, no martial arts moves work other than a handful of arm bars and rear naked chokes. I've used my Aikido as much or more than most of the other tools in my personal tool kit in a variety of altercations, your mileage may vary, it really doesn't matter what your opinion is, I'm not here to convert you to the faith of Aikido, I'm simply trying to explain the dissociation between what you are watching on TV and the system itself, if you are already of the mindset that Aikido is 100% garbage, I can't change that but it doesn't win you the argument either, its just your opinion.
Here's some more anecdotal information, I don't know what your experience level in actual violence is, as someone who has spent time in war, the ring and as a beat cop I can tell you that war is not a street fight and neither are the same as a duel in the ring between two athletes. There is a definitive difference between what you see on you tube and what goes on in the real world, when two people (or more) decide to do serious harm to each other. Now, it isn't going to win me this internet argument, but I can say with certainty that those stupid Aikido moves you say don't work have kept me and several of my friends from serious harm and its led to me being able to de-escalate and deal with violent encounters with real people in a way where neither of us got hurt, on many occasions. Does that mean my intellect, manhood or my kung fu is better than yours? No. What I will say is that there is perhaps more value in spending some time training with Aikido than you suggest, do with that what you will but if you can't say the same, do me the courtesy of thinking about that before you poo on my beloved art out of simple internet trolldom. Other than that, I think we are at an intellectual impasse as it stands since I'm not really wanting to preach and your not really wanting to have a productive conversation.