First being that the old way would allow you to using options mid-pitstop such as the chat function and changing audio or visual settings... because as it stands you have to either exit track or go into options while parked or auto-drive.
Secondly, you get to see the car physically travel down pitlane as opposed to be auto-warped (largely FAR too quickly) through pitlane thanks to a cutscene. A more realistic time for drive-through time, and pitting actually becomes a calculated risk.
Thirdly, while a Gimmicky aspect, it allowed option to run mixed compounds front and rear. Custom BoP series with FF vs. FR/MR can be spec'd with RHF/RSR setup on FFs as mandatory for them to make their tyre wear even as possible.