Being able to swap out weapons on death weakens team synergy and strategy, it removes the ability to make mental notes on the fly so as to create interesting/creative strategy to outplay an opponent.
I also believe that this will cause really weird gameplay, on every death a new build will be revised and it is rather likely that it will be a direct counter to that of your opponents. Players will be stuck in an infinite loop of counter builds, which results in a system where builds are more important than player skill, which doesnt really lead to anything interesting - atleast from my perspective.
Yes, this is pretty much how I feel about it. This would de-emphasize tactical decision-making in favour of build decisions during a match. Why come up with a better plan when you can blame your build?
Let's not even get into the potential RPS silliness this could lead to.
I'd also like to point out that with some of the examples Bridger used (LoL and Starcraft, I have no real experience with FPS games) these in-game adaptations you make aren't instant but very very gradual. Switching unit comp in SC has prerequisite tech and production facilities, as well as unit building time. In LoL major items require a lot of farming time. Build switching in GW2 would happen near instantly; you can't make a direct comparison.
Bridger says that he doesn't want to go into a game that's already imbalanced from the start due to build decisions. I can understand why he would feel that way, it is very frustrating to be disadvantage due to something you have no control over. IHowever, I believe that in GW2 any build disadvantage (within reason; some builds are total trash) can be overcome with superior tactics and teamwork. There's so much strategic depth involved with those 5v5 maps that I can't imagine builds being as big of a factor as in GW1. Even if, all else being equal, you lost purely due to a weakness in your build (unlikely) - you'll still get other chances to make up for it in a real tournament, where it's mostly best of X.
tl;dr: Bridger makes some valid points but introducing this causes more problems than it fixes