This is an odd way of putting it that makes it seem way worse than it is.
From the PS4's side of thing, essentially this is how it sees the circle button.
doing nothing: (constant stream of 'off')
000000000000000000000000000000000
dodging (super quick tap):
000000000000000010000000000000000
sprinting (significant hold of 'on')
000000000000111111111111111111111(etc)000
Now, sure, some people might have a heavy finger and hold down dodge a bit long and you'll get:
000000000000001110000000000000000
that Bloodborne will recognize as 'dodge'.
It's not that it's "waiting a moment" to see if you are still holding the button -- that implies it needs to wait until 'sprint hold' length before it can act. But actually, it can act on dodge the instant you release of the button. And we're not talking 'moments', we're talking miliseconds.
So honestly, I can't imagine this even affecting 99.9% of players at all... and imho, if you're fast enough on the draw to care about the milisecond you tap the button (and hit it that fast), then your release should also be super fast, and more importantly, your ability level should allow you to quickly come to terms with how it plays.
For us 99.9%? If you tap the button, you get what you want when you want it. Heck, I doubt most people will care (or notice) there's a tiny delay before you start sprinting.
Sorry for the late reply, and thanks for the explanation, it's very clear. However, I'm not sure it's correct. When at a neutral standing position, holding the dash/dodge button without letting go will result in nothing for a short moment, then a backstep dodge. In this scenario, the dodge input isn't letting go of the button as you explain, it's holding it for a certain amount of time. If it works differently while moving that's very clever and eliminates the need to wait for the full dash startup time, but it still creates some amount of unnecessary inherent lag because the input it's looking for is letting go of the button after a sufficiently short enough time of pressing it rather than the press itself. That's still not ideal.
Do you have proof that the game does interpret dodge inputs this way? I'd really like to see it, and know what your methodology for finding out was if you tested it yourself. Knowing whether dodging while moving works the same way as backstepping does or not is something you'd need either deep access to the game's software or some pretty serious or clever hardware to test it seems to me, so if you've got it, please show it off!
I don't really understand why you make excuses for the mechanism being flawed. A skilled player being able to overcome the flaw isn't a reason for the flaw to exist. I've felt its effects, and the game is surprisingly, even unreasonably demanding at times with dodge reactions. For example, the basic mob with a torch has that attack where he shoves the torch in your face; this attack has no real windup animation and deals damage within about 15 frames, and it's not the only attack like this. You can absolutely counteract this attack through means other than strict reaction, but making reaction bordering on physically impossible is just really bad design in the context of this game in my opinion.
I don't even think you're right to say that most players won't notice the startup lag for dodging and dashing, it's just that it's either subconscious or waved away as something else. Unfortunately there's no way to determine that without some broad survey of players so that whole argument should probably just be dropped.
If you want examples of dodge startup lag causing harm, the best thing I can give you is this crazy takedown of the Cleric Beast from my friend:
https://www.youtube.com/watch?v=J8w2kH5aFsc
I think we'd agree that his judgment is sound enough to tell when he pressed the dodge button, and both of the attacks he's hit by have noticable windup animations during which he's not doing anything that would stop him from dodging. I believe this is a real problem. If you have the means to test it with precision, I urge you to do so.
My perfect all Achievements/Trophies 'Souls' games run continues! 
thanks knitoe!