Does Avis not give you the ability at your status to walk down the aisle and pick a vehicle? I'm President's with Hertz and Executive with National (both via credit card bennies FYI...I only rent about twice a year) and I can't remember the last time I had to ever go to a counter to get issued a key unless it is such a small venue that there is no "pick and go" aisle. Your example is ORD where I will skip the counter in less than 2 weeks with National and take my pick.
No, Avis simply assigns a car and sends a text what stall it is in. One can change the vehicle from the Avis app, but often is no alternate vehicle available.
The assigning of the vehicle appears to be a manual function at the airport rental location. Some Avis airport locations, to include major airports, seem unable to assign the vehicle in advance. When this happens, the preferred renter is supposed to skip the main Avis counter and go to the Avis preferred kiosk in the garage. Issue is, you walk past the main counter, go to the garage, and often find the Avis preferred kiosk unmanned, so then you have to walk back to the main counter, and the line grew longer than when you walked by it five minutes earlier.
Not so long ago, I was renting up to five cars per week, most every week of the year. One starts to learn a few tricks to avoid lines, especially at smaller airports, where only one counter person may be present. One trick is don't go to the bathroom when you get off the plane, make a mad dash to the rental counter. A delay to the rental counter, even if a small delay, can risk an auto renter from having a person in front of you that has credit card problems, but won't leave the counter. I have seen police called to get people to leave with a non-working credit card.
Another is getting to the counter quickly because the rental location runs out of cars, first guy to the Avis counter off a flight gets a car, following guys in line don't. And finally, when no cars are available, play the DYKWIA card and show you are a President club member, show how many cars you have rented in the past year, and that you will take a "broken car". I have had locations with no working cars give me cars with major crack in windshield, accident damage, etc- by playing the DYKWIA card. And I hate playing that card, as I am a nobody like everyone else, but having a rental confirmation and no rental car available one goes to whatever it takes method in trying to get some wheels.
The reasons a rental car location runs out of cars is often because prior renters failed to return the car on time. There are numerous reasons a renter fails to return a car on time.