Personally, I did have very soft discouragement against wide-open 20% time. I asked around and a lot of people I talked to initially advised me against starting a 20% project so early, and especially against starting a new project rather than working on an existing one with engineers at a higher level than me. At least, they said, make sure I could get reviews out of it. That's not policy, but advice. People have their own theories about how best to get noticed and get promoted. Some of that has to do with 20% time. I guess if you're solely interested in promotion then you give more weight to such advice. I hope most Goolger's aren't solely interested in promotion.
I'm very glad I ignored that advice, both because I got to do very interesting things and because I got recognized for it, and I'm glad that I could ignore the advice because of our policy.