I looked into VW's "$199/mo" Tiguan lease not long ago and found it to be smoke and mirrors. It was only a 5000 mile a year lease.
I found Jeep's lease deals to be drastically higher than advertised as well when I actually started dealing.
I don't think I got a particularly good deal because it's a horrible time to car shop. I had two cars tank out on me and I replaced them with one car that I wanted but I don't feel like I got a steal. Toyota actually seemed to be affected the worst in my area by the shortage in terms of selling everything over MSRP.
Selling inventory over MSRP is a dealer choice. In the store I worked in, we refused to do it. The net result was that popular models often had a several month long waiting list. But for those who choose to do so, it certainly balances out supply and demand and results in product availability.
If dealers have product right now, it's because:
1. Their models are crappy and in low demand
2. They have chosen to sell their inventory in excess of MSRP
3. Their manufacturer has been able to obtain sufficient microchips to continue production
But even if #1 and #3 are the case, the lack of inventory elsewhere means they probably already sold what they have.
I know of several GM dealerships who have zero inventory and have been that way for a few months now.