It depends, i have heard of people just keep pouring money into there starter car because they liked it so much. However, if your not big into your starter car then I suggest against it. As soon as I unlocked the rx-7 at rep level 4 or 2 (not sure), I immediately traded my starter car out. It also depends on your driving style. If you want to add parts to your car that "lower" your horsepower (such as drift wheels and suspension) then keeping your starter car filled with the newest and best parts wont really give you enough "horsepower" to compete in many of those higher horsepower races(when u unlock them). Personally i kept up with my rx-7 until i reached rep level 16 where i then bought a 350z, which i built it for drift, which made the "horsepower" to low for me to compete/win many circuit events(depending on game difficulty). After I became frustrated with the power and what races allowed me to do what, I was debating on what car i could get that would be fast and that i could build for drift and circuit races(making my driving style fun yet still allowing me to compete). I bought a Evo 9 (which has stock 193 hp) which I upgraded and still use now that i ended the game.
Basically its up to the player. I didnt use any of the cars I won bc i couldnt modify how they looked, but dont be afraid to go buy a different car as soon as you unlocked it.
btw if you like your starter car but cant compete in higher tier races, try focusing on getting rep and then engine swapping it for allot more hp.
