I think the success of unlimited vacation really depends on the company, your manager, your peers, and you. That is a lot of things to get right, but if everything works out, I think unlimited vacation is really great. At least for my team, I think everyone shares the feelings that vacation is important, and people are good about taking it.
As you say, I do end up taking a lot of random days off, but that is in addition to longer vacations. I think thats the real advantage to unlimited vacation (when done correctly). If I want to take a random day or two off to take care of a backlog of errands, I just do it without a second thought. I don't have to worry about all these randoms days eating into my 1-2 week trips I have planned in the spring or fall or the 2 weeks around the christmas with my family.
Having said all that, this is my perspective and I am sure that there are probably people even within my own company that don't feel this way. The idea of a minimum policy sounds interesting. I wonder if that would lead to some people taking less because its tracked, but with other people taking more because they don't feel pressure not to.