I think a green in the middle of the green really forces people to consider what they think golf is all about.
If we think of golf as a skill game focusing on skill, it seems entirely antithetical. It is pretty ridiculous that we'd put a big penal barrier right in the center of the target, with effectively no strategic function other than forcing a bailout direction to one side instead of the other.
It's also complicated by the fact that, while we ought to be able to use any club at any point of the game, there is a sanctity of the green such that we are effectively required to only use a putter. Exposing this inherent contradiction in the rules can be unpleasant.
However, if we think of it as a skill game focusing on being a fun game, then it's entirely excusable. While it seems a bit pointless, it can be refreshing in suggesting players take a different strategy than they would otherwise take (say, play short of the bunker and accept the longer putt). It can also force very complex putting feats, that would otherwise not ever be attempted (here, I think the fun but absurd putt to get around
the Lion's Mouth on #9 at Lake Merced, which was clearly
intentionally designed).
---
Personally, I see bunkers inside greens as center-line bunkers on steroids. I think they should be used extremely sparingly, and the only place I see them serving positive function for both fun and tests of skill is placing them on 19th holes to increase scoring variance to settle tied matches, such as
#19 at Forest Dunes.