I think the practical reason for the difference between NA and EU is that it's The Way Things Are Done for both regions, and the exact events that led to things being that way were years before I joined this forum. Also NA has UGC for all the poors so making direct comparisons of ETF2L to RGL isn't right.
How would you implement a prizepool in EU? I think fewer people would quit than you say even if paid divs were the only options. There may or may not be room for a concurrent free league, but despite the amount of shit that gets talked about it, NA has sustained a free league in UGC this whole time, so I doubt that would be an issue. ETF2L itself could get in on running both types or not, but at the end of the day, all an EU prizepool means is that the EU community needs someone(s) it trusts enough to handle money to step up and distribute winnings.
If running two leagues really isn't viable for whatever reason, we could try to get crazy. What if you ran an entry fee bracket parallel to the normal free one? During the season you can simply run everything normally with all teams, and then I see a couple of routes for playoffs. I think the best is again to just run playoffs as normal, but only teams that paid in are eligible for payouts. So for example, if at the end of grand finals you had:
#1 Team 1 (free)
#2 Team 2 (paid)
#3 Team 3 (paid)
Team 1 would still be able to say they're the best team in EU, but since they didn't pay league fees Team 2 gets the grand prize, Team 3 would get the 2nd place payout, and so on. You could argue that only teams with a chance of winning would pay in, but that's kinda how things already work anyway, except right now there's absolutely no one paying because it isn't an option. You could argue that it makes grand finals less exciting if the prizepool might not actually be on the line, but again, compare to now, where no one gets paid.
As full alternatives, if you want to lock playoffs behind a paywall, or run separate free vs paid playoffs, you could have a secondary point total for paid teams during the regular season that only updates when they play against other teams in the paid bracket. Then you can rank paid teams separately in the postseason. But these have huge drawbacks, like the best teams potentially not technically winning the season because they didn't pay.
I dunno, at this point I'm just throwing ideas at the wall to see what sticks, but the point I'm trying to make is that there are plenty of options to try to implement if anyone really feels passionately about prizepools. My feeling is that there isn't one because the people in charge feel they don't need one, or maybe even that TF2 shouldn't have one, and I wouldn't fault them for either.