What's the alternative here? Let the company's schedule be determined by sporadic PTO usage that they are expected to have no control over?

Yeah, that's the idea. You give me time off, and you prepare around the dates I give you.

Or I'll find an employer that respects me as a person, and I'll quit by ust not showing up anymore because fuck you for denying my PTO request. Don't disrespect me while also telling me that you can't survive without me. You're just telling me that I can ruin things for you by leaving without notice, and giving me the motive to do it.