A UTO plan sounds enticing, but it wouldn't address individuals who are reluctant to take time off at all, leading to burnout. This is listed as Jacob's first "Con."
Perhaps a combination? A minimum number of annually expiring PTO days, with an open policy of UTO beyond that?
I agree this would be a major problem. It's one of the biggest problems listed with unlimited vacation, and that's when you're still getting money for it.
I think the underlying problem is the conflation of hours worked with value to the company. I think most people will be more productive for a company working reasonable hours for at most 50 weeks a year than working all 52 (minus holidays in both cases).
Accordingly, I think it is appropriate for a company to pay you to not work some of the time. I think that fits with your suggestion pretty well: give an employee 4 weeks PTO (or whatever you think will optimize their productivity and happiness), with the option to take more UTO that might not be an upside for the company.
edit: There should probably still be some reasonable cap on the additional UTO. Not pay their salary during vacation still doesn't account for fixed costs like health insurance and office space. In practice I don't think most people would take enough UTO for this to be a real issue, especially with the work culture in the U.S.
Perhaps a combination? A minimum number of annually expiring PTO days, with an open policy of UTO beyond that?