The way you've described it sounds a lot more like CoD than TF2. Which is a good thing. No medic, no "That one guy have access to only 2-3 unique weapons" kind of boringness. I can understand why it's there and how it works well for a game of that genre like TF2, but I'd really hoped the game developers would drop it now, something fluid is always better, perks, abilities and whatnot decided by the player himself.
Not necessarily. It's quite possible to create a 'best' class/loadout like that.
Example: Bad company 2 medic class. Some of their machine guns are so good in combination with their heavy armor and healthpacks/defibs that in many servers, you'll see 70% of the players using a medic. The specific perks of the assault class and other classes are often dwarfed the all-round usefulness of a well-equipped medic (depending on map, of course).
I can imagine a situation like this happening with your proposed class system very easily. All-round almost always > specialized, therefore you'll see everyone running around with similar if not identical loadouts.
I like a game where a Medic can't also be on the frontlines dishing out the pain, or where a sniper can't carry a shotgun to get up close.
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As for the game itself, I'm not entirely convinced, sort of like Bulletstorm. The idea itself sounds fun, but I have my doubts about the execution of these ideas. Both games sound quite a lot like they promote a playstyle that's very figured-out already: what you're supposed to be doing and how is immediately clear, the only discerning quality between players is how well they do it. Many modern FPS games suffer from this, I'm just hoping these won't.