Someone that is in the prime of their career bringing a wealth of experience could probably walk away from a position that only pays for Y travel. Someone younger and/or being given a chance at acquiring new, in demand skills should tone it down and not even ask. If its Y then its Y. Suck up the skills and experience and ultimately if appropriate and optimal look for greener pastures.

Moreover, some companies are more flexible with travel. One might be able to travel a day ahead to rest up. Even flying in J longhaul can take it out of you. Some companies are open to an extra PTO day after long travel.