I read most of the thread while at work, sorry if I missed some arguments but I wanted to give my personal opinion. It's really an interesting debate.
To me, rerolling into "someone else" every time I'm asked to or every time it's required is a non sense. As a player in a RPG, I made a choice to create a certain character when I jumped in game. I expect my character to be good at performing the actions I wanted him to be specialized in. And I should be weaker than others in doing other types of actions. Weaker but not unable, and that's why all weapons can be used even without specialization in AoP, and that's why I can raise my other skills quite high with leveling.
Being able to reroll for free destroys the whole thing of being good at something, and be known for being good at something. It's good to know someone who is a great tank, who played countless hours at this role and who enjoys doing his job better than the opposing tanks. As a character of this world, and as a player, I want to fit a role that I chose, and be asked for help because I'm needed.
When high level characters reroll, they just stick to the most advanced equipment that their specialization encourages to use, and never use the middle stuff. It's kinda missing a part of the content imho, even though this is mostly a matter of taste and also is highly depending on the game mechanics related to equipment crafting, which are going to evolve a lot in next season.
Another matter of taste, but imho you have to "deserve" your character, and his capabilities you chose to master. You should always have spent time getting those skills, evolving, getting experience along the way. You want new ones? You should make a new character. Now, being limited to centaur bashing to get a new HL character is an absolute stupidity, and if the game cannot offer a more dense leveling experience, I agree this isn't an option (and so far, it wasn't).
About being able to counter your enemies when necessary, I of course lack actual HL pvp experience on AoP, but it seems extremely strange to me that with the variety of weapons, maps and items in general available, a team cannot find a way to beat any opposing team, whatever build they chose on their side. Not even considering that without mass reroll, teams couldn't elaborate such extreme character roasters, which would limit the need for the opposing team to do the same. Instead we would have teams with different strategies based on the available players. Of course I know about sharing chars, and doing alts. But that would probably still limit the phenomenon.
Two last points:
Being able to reroll for free makes it also harder for the noob to master his playstyle, since he has often to change to fit to the group.
And of course, the process of rerolling all the time is annoying in itself.
Now, I also agree with some of the points in favor of (free) rerolling. It's good to be able to fix a mistake you made with your build, or to change your playstyle altogether once in a while, without the necessary need for a new character. In extremely critical situations, such as the domination of another faction, it would also be nice to be able to reroll a squad to try something different against your enemy.
For those reasons, I think rerolling should be limited. Something satisfying for me would be to grant every fresh character 3 free rerolls, then allow more rerolls as long as the player pays the price. 500 caps for example for the first one, then it would skyrocket based on a variable that increases with each further reroll, and decreases with time.