There were about 60k bus trips per day in Southampton pre covid I believe.
I don't have exact figures sure, but say all those trips were 2 way, that's 30k people a day.
If maybe 1/3 of them are travelling to the city centre for a start between 8.30 & 9.30 that is 10k per day.

At rush hour.
A standard carriage way moves about 2k per hour, so if they all drove that would either mean providing 5 more lanes into the city, or longer tailbacks.
You'd also need 5 more lanes out of the city.

So if anyone can point out where 10 more lanes an be fitted in, coming into the city, to be up and running within the month I'm sure that the council will love to hear from you.

You may have noticed though that 14k people/hour on bikes can fit on a carriageway the same size..
So if people can be pursuaded to ride it makes the problem far easier to solve.

Now here's the clever bit.
Most of the roads coming in to the city look as if they are 2 lanes or more, but if you look closer most of them are actually at one point or another single lane, so their effective capacity is capped by this one lane section, this is the A3024 for eg

This means that all the extra space before and after this point is only ever used to store the queue of traffic until it goes through the pinch point. Instead of storing idling cars it can be used for bike lanes, making cycling massively more attractive and maybe

just maybe, helping encourage some of the people onto bikes instead of into cars, so making our city centre that little bit more livable...