EA actually have put themselves out doing this
unlike GTA Online where Rockstar live off revenue generated from it, EA could just sell the game through Origin and dlcs while Revive hosted the servers which benefitted everyone as EA gets the cash they want and the players get their online
If it was that easy to put it back on Origin, they could've easily made their own servers themselves - however, not that many people would've paid for it anyway, nor it would've been enough to keep them up (Or atleast keep those greedy bastards profiting) - thus why they got closed/never restored in the first place. They didn't even let the old Multiplay BFH community servers remain up, when they were the ones hosting more than half of the servers back then.
Revive had made it as free as it can be, especially BFHeroes (atleast if we exclude the idea that the revive community was paying the servers on their own, but no member was ever forced to pay for their servers, or anything, to play).
Even if they were basically promoting these old titles, EA simply had to respond because if they don't protect their IP, it can easily be snitched off within a few years - they were fully and legally allowed to do so.
But then again... Fuck EA for doing this. This is why I don't touch any new product with their logo.