For shits and giggles I looked up what a Lyft costs from Paris to LVMS and its $30 one way, but that is also on a Wednesday night, I can imagine its at the very least double that for the weekend. When its all said and done it might be the same amount but at least with the rental car if you decide to go somewhere else you can do it easily.
I know it is probably too late to change hotel plans but if you go again, look at Cannery. Its off strip and a lot closer to the track and anything on the strip or even Fremont St. Its right off I-15 or even a straight shot down Craig Rd to Nellis Blvd which will take you in the back way into the track.
First time I went to LVMS was the fall 2020 race and it was the first time I had ever been to Vegas itself. Stayed at New York New York and by the end of the weekend I determined it will be the very last time I stay on strip when going to the races, too much of a hassle getting in and out especially returning to the hotel during prime-time hours. Ever since I have either stayed at Cannery or found an AirBnB in north Vegas.