If we want to run with the philosophy that paying real money for these things should mean that they go straight to our garages rather than having to first buy them from the in-game dealership with game credits, this would then logically suggest that all of the cars in the entire game should just go straight to our garages on the day that we pay for the game.
The only difference between the cars that came with what you paid for at the store and the cars that you paid for as DLC is where you got the files from and not whether or not you paid for them. You paid for the first 1000+ and then paid again (hypothetically speaking) for the cars from the DLC. If paying for them with real money means they should instantly go to our garages, all of the game's original cars should also have went straight there since we paid for those with real money, too.