It was not that difficult to pop these off. I remember as a kid getting 2 of these for Christmas. Therefore I decided to have a little fun with them and popped off the models (the inside one being a little more difficult) and swapped them around. I also pretended to drive the little plastic cars around even though there were no wheels on them.
This is one of the prime examples of models from the Lesney era with a lot of plastic that I remember as a kid thinking the same and not worrying about it. This is why now when I see models that have a lot of plastic I do not worry. I simply remember back to when I was 7 or 8 years old and thinking Matchbox had a lot of plastic in them and not caring.
I do not think I even have the old Car Transporters any more. I believe I ended up with 3 in total that I swapped vehicles around on. I ended up with one Transporter with all red cars, one with all yellow and one all blue. Even as a kid I was careful to pop them off so that they could be popped back on again and not fall off. It does work if you have a little time and patience.