I feel like I would hate this. Right now, I get 5 weeks of vacation time a year (been in my job a long time, I would max out at one more week though I'm a few years off from that). I also get 5 paid sick days a year, and 7 paid personal days a year. So in total, I get 7 weeks and 2 days off a year paid. The personal and sick days expire if not used by the end of the year, so everyone uses them. The vacation carries over, but you can only accrue up to 150% of your time. (This year I'm carrying over about 3 weeks of my 5 weeks, so I'll have around 10.5 weeks to use next year which is pretty cool.
I rarely carry more than a few days over, this has been a weird year. I never leave any personal or sick days unused. Because I have this amount of time, and it is my time, there's an expectation that I'll use it, or at least no one feels like I'm doing anything wrong by doing so. Some people carry over more of their vacation from year to year, but at a certain point you have to use it, and as its one of our benefits, people do. I've never felt bad using time and no one has ever tried to make me feel bad for doing so.
Unlimited sounds great, except that changes the culture completely. Sure, no one's going to give you a hard time for using a day or two here or there most likely. If you use too much though they definitely could come down on you for abusing it. Even if they don't though, even if they're great and understanding and really don't mind you using this benefit they have given you, I would constantly feel worried that I was abusing it, or fear that they would come down on me for doing so, even if evidence suggested they probably wouldn't. Every day I took off would suddenly come with stress, with me wondering if what I was doing was okay. That sounds miserable.
If you think people need to have more time or need to feel less worried about using their time, just give them more so they don't constantly feel up against things. Don't create a situation where there either have to become unwritten rules (because after all, people can't keep getting paid if they take every day off forever) or where people constantly have to worry that they exist even if they really don't.