We bought a cheap TomTom in America last year, far cheaper than renting one with the car (about $10 a day if I remember).
One problem I had with that was that I can't update the maps at home here in the UK because when I log on to the TomTom site it doesn't recognize the model that I got in the US. I tried emailing them a week before going to California last month and was given a case number but never got an answer despite repeatedly asking them and quoting the case number and telling them that I really needed to get it sorted before departing.
We used it with little bother in spite of the fact that it was out of date, but the bastard thing kept on telling me to update it as it was insisting that it was 18 months out of date.
As a matter of fact I did try to update it in one of the hotels, it was going to take three hours to download to the computer, that's right- the hotel's computer, and after that I was to reconnect the TomTom to it for another three hours for it to load. Well, balls to that, I certainly wasn't going to sit by the computer in the hotel foyer for three hours of my holiday. And of course it carried on reminding me regularly that it needed updating for the rest of the trip.
Another problem we had happened in San Francisco where it kept on losing its signal, SF is very hilly and Downtown in the streets between the tall buildings it kept on jumping about and getting lost, and it was totally useless when we tried to find Twin Peaks and we just gave up. Now whether that was the fault of the bargain-basement model or not I don't know- perhaps their top-of-the-range model might have been just the same, but I thought I'd mention it. Likewise the issue with the screen brightness; we had rented an open-top Mustang and the screen was difficult to read when we had the top down, but again perhaps I was expecting too much.
As for being unable to play with the fixed Sat Navs, we have had a few in the past but I don't remember that being the case. You could get lucky and find your car comes equipped with one despite not having rented one.