As someone fluent in officialese, allow me to translate into English:
"...high patronage results in several thousand bus movements per day on Princes Street and crowded bus stops across the city"
A major reorganisations of bus routes through the city centre is in the offing.
"I would expect us to look at having fewer private cars and better public transport"
Expect us to look - I am committed to nothing.
"We need to make sure people can still access the city centre, but in a way that maximises space"
We might pedestrianise a small area (bets on parts of George Street).
"We’ve spent a lot of time with Lothian Buses looking at Princes Street, George Street and Queen Street and how their routes across the city centre work"
See above.
"We’re not aiming to eradicate private cars, that would be ridiculous"
Drivers - no need to panic.
"Everybody has to acknowledge that you cannot drive everywhere all the time"
The pedestrianisation may be time limited - like the roaring success that is Rose Street.
"This isn’t about the council deciding what will happen".
Don't blame us.
"This project aims to improve conditions for access for pedestrians, cyclists and public transport".
Aims to improve - no commitment to action
It looks like this is really about the George Street project and facilitating the movement of huge numbers of tourists about the city centre.