The intent is great - to improve gameplay in realtime. I only play realtime and it is a bit frustrating having very slow solvers on the table, so I understand where this idea comes from.
As yuniboshi said, BGA does not always bring everyone into the game together. Webpage, browser, and local internet issues can all mess up someone's initial access to any game. As someone who is often late to the first round of any game due to factors beyond my control, I am grateful that the BGA community accepts and allows for these struggles!
Like Romain627, I play in realtime but sometimes have something else incidental that I am doing between rounds. I also like to pause and remind myself what is involved in each scenario before I hit start. AND I kinda like starting a few seconds later than others as it psychologically reduces my stress and helps me focus. So I greatly appreciate being able to run individual timers.
ALTERNATIVE:
We still have the rightly-identified problem of slow solvers holding up tables in realtime. A simple solution already exists:
There seems to be a code of honour among most players that we'll forfeit a round if our timer runs out. This means there's no need to boot a player and neutralise results. Simply capping Fast Mode at 2mins instead of 3mins means those of us who want to play hard can easily do so - while leaving slower options accessible.
Also like Romain672, I do actually like the idea and thoughts behind it. I especially like the idea of a timer that starts when the first person solves the puzzle. I can imagine this mode would be especially exciting on very large tables! I just think there are some major problems involved as well.
So, by all means, keep developing Blitz Mode as an option. I'll happily give it a try and see what I think in practice! But perhaps also consider shortening the timers on Fast Mode to produce a less dramatic solution to the difficulty?