I've gotten and/or seen operational upgrades when the lowest level of car was reserved and not taken. They have to give you something. I dunno about *asking* for it in most cases, because if you *want* it, they will try to charge you for it. If they have nothing left to give you, then you may get something for free.
My recent example was a Priceline booking, actually, at LGA Hertz. Bid on cheapest whatever, only $30/day when going rate was $70 (weekend in HOT last August, everyone wanted a car to get out of NYC). That should have been compact or subcompact, but they gave me the Mustang that was parked right outside the door. Dunno if it helped that I came in at 6am or what. But it worked. They may have had trouble selling that kind of upgrade anyway.
A decade ago or so in Florida it was same thing, at Budget at TPA. Rented cheapest economy, got Mustang, with V8 even.
I think operational upgrade can be fairly common in rentals (I don't rent nearly enough to know how common), but I certainly wouldn't rent lower assuming I could get the upgrade. It's quite possible you could get a better deal on the higher class of car if you book that in advance than you would get if you have to pay to upgrade it after you've booked the econ/compact.