Thanks Hobusu for detailed examples. Now we got some scenarios to analyze 
Okay, so first, can we agree that outside of jump in’s people are usually not just standing near each other and not pressing buttons? Feel free to correct me on this of course, but I think we can ignore this scenario for the sake of this argument and thus focus on the dynamics of jump ins
The scenario you mentioned was after jump in and I’d agree this is the closest we will get to both being close but not necessarily moving, so let’s analyse this a bit further 
We have two ways that could happen I think. Either Player A makes an empty jump and then tries to throw or he jump attacks and tries to throw after the block stun ends (let me know if there’s one I’m missing though).
In case one, player A empty jumps, player B most likely blocks (holds backward) and then gets caught with a throw, cause he didn’t anticipate the empty jump. Here, neither option would make a difference, since he’s not gonna react to the empty jump either way.
Case two would be Player A jumping in and attacking and then trying to throw after the block stun ends. This is where the main difference is, IMO. In case of no throw button what will happen is. Player A jump attacks, then either 2.a) presses fA too early and gets and attack animation out, while player B will buffer the throw and throw player A right after he comes out of blockstun becase the throw start up frames are way lower than any fA attack startup frames.
or 2.b) happens which is, player A waits a bit for blockstun to finish before he tries to throw, but then also Player B will most likely get the throw because his timing will be frame perfect (because he buffers the throw) and Player A’s most likely wont be (because he has to manually time it)
(this is also an okay option select sorta, because if A does an attack string the throw won’t come out to begin with and you keep blocking, you only throw if your opponent tries to throw and then you automatically win)
But since player A knows that he can also do 2.c) wait in neutral for a bit longer after landing in case B does this option select, in which case he will either YC B’s throw or if B doesn’t do that and just presses back for blocking he can still get thrown by A with fA
(but of course since B knows that as well, he can instead go neutral real quick before hitting fA instead of buffering his option select to catch out A’s delayed option and thus we have a cool mindgame again)
If there was a throw button it would go differently. player A would try and startup the throw in such a way that the active frames are active just after hit stun is over, in which case he either 3.a) times it right and gets the throw because B will just be out of block stun and start up his throw or 3.b) he times the throw too early, the throw misses cause B is still in block stun and A gets thrown instead after B comes out of blockstun
In scenario 3.c) A times it slightly too late such that A throw starts up while B’s throw is active in which case B throws A
or we have 3.d) which is what you’re talking about I think, A is way too late and gets the Yomi Counter because his timing was off by too much, such that his throw didn’t even start up before B’s throw hit its active frames.
Here too ofc both can consciously decide to delay their throws juuust a little bit to catch the other out on purpose, and ofc, if one anticipates that he can just neutral A for a 2 hit combo
But notably no scenario includes anyone pressing buttons quicker in a “having quicker fingers” kind of sense, since all the decisions of whether to press a button or not to press a button happen early enough, that one can either do it as an input “string” where there’s no downtime or then it’s a buffered throw which will come out on frame 1 of being in neutral or then it’s a timing thing where one can mistime his button presses and get lucky, but also one can purposefully delay a button press to bait the YC (which is fair game, I think)
I think the main difference of throw button vs no throw button is what TYPE of pressure one can have after a jump in attack and how the dynamic goes between the one who blocks and the one who jumped in and what options either have.
And since GRAG mentioned option selects, currently there’s the one I mentioned above (the 2a) 2b) )already in the game and is easy to execute if one wants to. Then there’s the timed delay where you go into neutral for a split second before pressing buttons, but quick enough that you can still block if need be, which works on either scenario (and also beats multiple options). So I don’t think we’ll get rid of option selects (some are just hard to time), but having them in also leads to next level mindgames, so I kinda don’t mind it either way.
And as for the “correct” way to throw, the same would then be true currently that the “correct” way then would be to just tap forward/backward the moment you hit A and not hold it (which is just as awkward).
So in summary, the only scenario I think where being slower is better with throw button would be 3d) which can happen on accident, because the timing window is quite small. On the other hand it can also be treated as a “time-crossup” where the player executing it can’t be sure if it ends up coming out on time or slightly delayed (like in a crossup where you can’t be sure if they need to block left or right). Of course B knows the timing is precise and A might not be delayed and so can then just delay as well, which again can be beaten by a well timed neutral A and thus we have the mindgame originally intended for YCs I think.
The main difference between having a throw button or not would be whether A can more quickly apply pressure by threatening to throw of whether he needs to wait a bit, cause he can’t win the throw timing vs B after a jump in currently.