Now, now...I don't think anyone said that having more time doesn't allow for better chess play. This is just a strawman argument you are building.
I won't play bullet for this reason. I suspect that I could be quite good at it with sufficient practice. But, I know that time management would take priority over good chess play.
However, guys...
When you do rated tactical problems, time becomes a serious factor. Not nearly as much as in bullet...though, I think, more at a slower blitz rate.
As a senior citizen, I am still sharp witted. But I do feel the time pressure. And, it is my experience, that usually you can solve the riddle within the time constraint (or slightly over) or...you will either get it wrong or seriously eat up the clock and still get strapped into the dunking chair.
Quick witted vs. dullard. My experience is that dullards have a serious problem with being quick witted. (Now, obviously, a couple of you guys may be the exception. lol)
All this aside...no, you have not convinced me that a class E player on rated tactics can be a class B player on any unaided chess play, regardless of time allocations.
Please come up with more reasoned rationalizing. (BTW...look up the word "rationalize" -- it is the exact opposite of what most people think.)
But, the thing does come down to tactics.
How can someone be terrible at tactics but an ace at anything else?
(Of course, I am excluding speed chess where time is often more important than tactics. Quick garbage moves may actually be a winning factor in bullet.)
To be honest I don`t understand your concerns. The Computer4-Impossible (rating 2050-2100) lost a 15/10 game to me although 5.6% of my moves were inaccuracies, 31.9% mistakes, and 1.4% blunders. If my every move were a puzzle I would fail 4 out of 10 (including opening moves). And I had much more time to think than I would have had with the Tactics Trainer.
You have to find and make the best possible moves to pass the tactics puzzles but you don`t need it to win a game. Your forum made me check many puzzles and you can often gain a decisive material advantage (=failed) or mate in 2 or 3 moves/gain a better advantage. If I played you I would likely capture your hanging queen without even trying to find a checkmate in three.
No offense meant, but I do not think 1600-1800 rated players (see your first post) usually play like aces which doesn`t have to apply to Bullet for I have no experience with this rating range.