My guess is that most of that heat is coming from your living space as opposed to solar heat gain. A lot of times attics are hot because there aren't perfect seals and warm living space air infiltrates through the cracks. If that's the issue, you could air seal the joints. If this is your issue, it definitely would not make sense to recirculate that air.
If it really is solar heat gain that's keeping the attic warm, I wouldn't do anything. Since the temperature change from living space to attic is going to be low so you will lose heat really slowly. That's always nice in the winter.
I sealed all top plates and penetrations with foam before adding r40 cellulose over existing fiberglass, so it really is solar gain. Plus, the house is cooler than the attic which is why I asked about reverse venting.
Good point about reduced thermal loss during the daytime, but at night the attic quickly cools off.
Sounds like the biggest issue would be dust so I'd need a filtered vent, and besides that might not be worth the price
I don't anticipate moisture issues, since the existing fiberglass looked fine... Of course if there is a leak all bets are off
BTW, I said "winter", but it's still sunny with highs of 75 around here. That's great but my house is 61 in the morning, and doesn't heat up quickly during the day.