If you plan on making a career out of the military, is there any downside to reenlisting for 6 years?

The only negative reason that I can imagine would be if you're given any sort of incentives to reenlist, like assignments of choice, retention bonuses, etc. The longer term of your reenlistments, the fewer opportunities you have to take advantage of the incentives. I suspect those incentives would disappear beyond some career stage though.

All my extensions were for 6.

I made the huge mistake of reenlisting for six years at a time and completed 30 years. I found out way too late that it's best to extend or enlist for the least amount of time possible, especially in the beginning of your career. I missed out on reenlistment bonuses because I always enlisted for 6 years and when bonuses were available I couldn't reenlist to take advantage of them.