I've been working on venting my attic. It's a 1950s build with gable vents and a temperature-controlled fan. That made sense in the pre-ac days to push 130F attic air out, pull 80F house air through a popped attic door, and pull 90F air into the house (or 70+F night air in), I guess, but with retrofitted ac, it's not appropriate.

Nowadays, you want the attic to breathe and hopefully stay ambient. Luckily, the house came with a recent addition of a ridge vent. Unluckily, there's no soffit vents, so the air is still pretty stagnant. I don't use the fan because it's mostly pulling air from the gable vents near the ridge and pulling some from small gaps in the living space ceiling. If you pull from the living space, as others noted with your crawl space, the air must be replaced with outside air, so you have to determine if that's a benefit or a negative. I'm working on adding soffit vents to allow convection currents to flow and give the fan much more outside air availability (along with sealing ceiling openings). While my rafters sit over the wall top plates and provide a 5" gap between them to the soffit eaves , the last installation of batt insulation was rolled up and taped into the rafter bays - just like yours. That's an annoying thing to undo every 16" in hot, dusty, mildewy, rodent-contaminated conditions. I've compromised by cutting the soffit vent openings and poking the insulation with a rod from outside the house. I've wedged some foam rafter baffles in the bays to make sure they stay open, even though they're really meant for blown-in insulation rather than batts. I've used the 16" rectangular individual soffit vents so far, but I'm starting to think I can tackle replacing the soffit panels with vented panels myself while tackling some rotting trim at the same time.

I live where it snows in winter and while this will make the attic cooler, it's supposedly still a benefit to help reduce humidity and circulate air to reduce mustiness. What I know for sure is my gas heat can keep up, my electric ac cannot.

My version of your powered vent is, with a full/sealed basement, I've propped the door with a fan to blow basement air into the living space and hopefully exchange air downwards. That's a relatively close loop, if it worked at all, by exchanging air between two air groups already in near contact via the floor. Agreeing with others, I don't think it should be used for the attic air. But your setup could be a good start to test the effectiveness of the fan and to be a step towards a better solution.

Good luck. Stay cool. Building standards have changed a lot in the last 100 years. I can't wait to find out what common practice today gets ridiculed in 50 years. My bet is on spray-in wall insulation.