No story per se, but a more in depth campaign is definitely needed.
See, this is the sort of thing you can do in a racing game to be more engaging and without being corny/hollywood
https://www.gtplanet.net/f1-2020-myteam-20200616/
Now I'm 100% NOT saying I think GT should implement something exactly like that, or even vaguely similar, but it's a good example of how you can make "just doing races" far more interesting and rewarding, more-so than just picking events from a soulless list and winning them...just because.
Clicking Sunday cup, picking any race, restarting until you get gold, choosing another event like FF challenge, completing 2 races etc etc... "Soulless" was perfectly put.
GT league and previous GT games campaign felt like quick play with restrictions.
The campaign should involve a sort of season system. If I commit to an event, I have to race the tracks in order, go through practice and qualifying (optional), and my final standings should be based on the event as a whole. If I want to play a different event, then I forfiet my current event.
Now, if I start with a stock Megane RS for example, and want to enter a GT3 event, providing my rating as a driver throughout my seasons is high enough, or I hold the correct license, and providing I can customize my Megane to specifications, I can enter that car into the event, rather than being forced to buy from a list of pre-made GT3 cars - which you also CAN do if you want.
Of course as you progress you need to buy higher end cars.
Speaking of driver rating, I don't like they way I can do a ton of arcade races and level up my driver rating for campaign. I'm a ruby driver and can take part in the professional league when I potentially haven't done a single beginner league race. It doesn't make sense. The campaign needs to have its own seperate system that involves starting from low leagues and having to earn your right to move on to the higher leagues.
Also I hate that you select a race, and are immediately just thrown into a rolling start. I want the real feeling of a 'race day'! Instead of a 'Story', the whole event could be brought to life. Start me in the pits, have my car delivered by truck and unveiled, have my engineer talk to me about setups and have him change them in the garage, while i put on my helmet and gloves, open my car door and get in and drive out of the pit garage.
Immerse me into the world of motorsport a bit more.