I rented a couple of Escalades, albeit in SLC, and they were not stolen. They are very, very nice; of the large SUVs they are my favorite.
I was watching a video on YouTube not too long ago, and a good way to prevent others from stealing your car is to remove one of the important relays from the fuse box (e.g., the fuel injection, ignition). If you just remove a fuse, any thief could figure that out and pop one back in. That said, have an awareness of your surroundings; I really don't think this will be necessary, but here is the video if you'd like to watch. I have never had a rental car stolen in over 10 years of renting.
If you book Luxury SUV, I believe Hertz will assign you the vehicle and it's generally the Escalade or a Lincoln Navigator (which is also very nice and I think does a little better on gas). I've never booked a specific class with National (and never used Alamo) so I can't comment as to those.
-J.