I actually thought about this this morning in the shower. I expect to get a lot of hate for my suggestions, but this is what my personal ideal Gran Turismo would look like.
Main interface screen is a 3D rendering of an apartment with a couch, a TV (this will be Gran Turismo TV), an open laptop on a desk, a view out over a nondescript developed city and a small phone table by the door with a set of car keys on it. An info box pops up with "You have a new email, check your laptop for new messages". You click on the laptop and a representation of a computer screen appears, eventually this will be a shortcut to all areas of the game similar in concept to the main UI screen we have now, for now only email is accessible. The new message welcomes the player as the new member of 'x' racing team, your courtesy car is in your garage and please meet us at the track for your first test session.
The player leaves the apartment by clicking on the car keys, then driving via an open world hub city (small-ish) to the local track. The city downtown has all the dealerships, the suburbs have tuner garages, there is a local 'test track' and drag strip, and the expressway out of the city leads to a toll station where a menu prompts tithe player which world / GT / city track they would like to practise at. The city needs to be fun to drive round, not too big and most of all, you should be able to bypass it all via your computer screen when you're bored of it.
Once the appointment is made at the local test track, the career mode is started where the driver embarks on a race career and as he gets more famous will be invited on to motoring shows for crazy events, to do photo shoots in magazines, timed laps in new cars for manufacturers etc.. (think of what someone like Jason Plato gets paid to do; Fifth Gear, BTCC, in magazines) all as a celebrity racing driver, now think of the overlap this has with the kind of A-spec events we get now and kind of imagine them dotted along the 'career path' of the player.
Naturally you'll have to earn licenses to race at the highest levels and you should get walk around garages as part of the hub city concept, but all of the grind and progression should be hidden and organic.
Anyway, TL; DR. Make game better, duh.