Sometimes I wonder how much of the problem is the "P" in PTO. When you're paid not to work, you're effectively getting a bonus -- being paid more for the time you do work. This also makes it a hot button for labor law -- if you leave with unused PTO, you need to be paid for it. Because it was never really about the time off. It was about the money.
Instead, what about simply having "UTO" -- unpaid time off? Take as much time as you need or want. Everyone will understand you're not getting something "extra" they're not getting. You're simply choosing to work somewhat less and to be paid somewhat less.
And to be clear, if an organization switched from PTO to UTO, they should give a one-time equivalent raise to make people whole.
I definitely don't claim this will resolve all the issues (humans in an organization will always find something upsetting). But wouldn't it eliminate a very big chunk of the ill will?