As an owner of a pool with an autocover I've had the same thoughts. However while the pool is in use/open the need for CYA isn't any different than a pool without an autocover so I can't personally see going below 30. Most of the time if we have people in the pool the pool is open and in full sun all afternoon.
Unfortunately my first opening of the new to me pool last year had CYA well over 200 and I gave up after getting it to 70 and used it at that level, this year I'm down to 45, but mainly because of the autocover I'm planning to work down to 30 eventually, although if I have to raise the FC noticeably higher than normal just to last a full day of being open I will keep CYA higher. I figure if I maintain it at 30 I can only use 4-6 pucks a year, which will make that 40lb tub I bought before the first opening and before I knew better last over a decade...