The computer beeping is merely a reminder and I'm betting most drivers will even disregard it after they are familiar with the track they are on. Gear changes happen so often and so quickly that waiting for a computer to tell you when to shift is a sure sign of unfamiliarity with the track layout and it's also a hit to one's concentration (ex. if they're trying to pass the car ahead or block the one behind). Anyone that does any sort of track driving consistently should know what gear their car should be in for each corner long before a race.
I'm not sure I agree, if they served no purpose the engineers would remove them. I think when they are in 'lift and coast' the gear changes are different, and I'd guess when they turn the engine modes up they would change again.
