Why does the car I'm currently driving spawn a lot more?

According to this thread

The problem lies in the loading and unloading of vehicle models. Apparently, each vehicle is so detailed that the system can only afford to have a small number of models on tap. This "reserve" of models changes based on your vehicle, location, and time. Vehicle models are also loaded and unloaded each time the view is panned or changed. If you ever notice looking down and empty street... Turn around, turn back around, and now that street is full of cars within seconds. That's just the games mechanics coupled with limitations of the consoles. So when you steal a car you can pretty much always expect to see your ride becoming very popular on the roadways.

Though it does refer this problem to console versions.
They could implement this workaround on PCs as well for low-grade PCs to run the game, but this is just speculation.

From this Gamefaq (the last question at the last section of the page). It relates to GTA IV, but is fairly relevant still.

I really wanted to drive and when I first drove it, suddenly a whole bunch of them appeared! How is that possible?

The FAQ states that:

Simple Answer: it is to speed up rendering speed. If every car you passed by was 100% different than the car behind it and infront of it dont you think it would slow the game down? they place alot of variations of the same vehicle your driving to prevent the game from slowing down due to loading.

The FAQ continues with a more complex in-depth answer as well:

Basically, the car models are too detailed for the RAGE engine to keep all of them cached and available to show up at any given time. So only a few cars are loaded into memory to spawn. But since the game has to have the car you're driving in cache, that puts it on a relatively short list of available cars to spawn, so all of a sudden everyone's got an Infernus.