I find it already unethical for lawyers to take a percentage of the awarded damages, a practice which is fortunately illegal in many European countries.
Why do you think that's unethical? Doesn't it give lawyers the incentive to fight for their clients? What if a poor client cannot pay upfront and percentage of winnings is what convinces a lawyer to fight in the first place?
Because it gives lawyers a stronger incentive to escalate conflicts, instead of deescalating them, which is not in the interest of society. Lawyering up is a zero-sum game, so the economy is better off if the money in question stays in a productive sector.
Take a divorce, for example. Do you prefer lawyers to have an incentive to say "calm down, I'll talk to the other lawyer, and we will find a fair deal" or "give me 20% and I'll make that bitch suffer"?
Note that a poor client who cannot pay upfront can still agree to pay after they win, just not a percentage of the awarded sum.
Escalating conflict may be a way of increasing the perceived uncertainty, cost, and risk to the other party, and thus increasing the likelihood and size of a settlement to make the case go away, so there may be an incentive to escalate conflict with contingency. Its probably less than with hourly fees, and more than with flat-rate fees (which ISTR are occasionally offered by some for some things like simple divorces.)