Many cities already successfully pulled this off and this method received far more popular support than just cutting off car traffic and expecting the people to "deal with it" without having good options.
1. You can't take away personal car access; the public transportation sucks! Make it better, first.
2. You can't improve public transportation; everybody drives so it's not a good cost investment. Get more people to ride transit, first.
3. Goto 1
You collect the returns after you invest. Otherwise almost any initiative would get bogged down into your 3 point loop. When companies build a new HQ they don't tear down the old one first. The "loop" is a fake conundrum.
For example, in western Washington, we've repeatedly voted to tax ourselves for transit. Our regional leaders had to push, prod, and beg our state elected leaders to pass laws permitting us to have those votes. (Meanwhile, road projects sail through.) Yet, more often than not, we've voted yes. But in November, through our tediously broken initiative system, the entire state will get to vote on whether to repeal our locally-approved taxing authority because a political shyster likes running bumper-sticker-politics campaigns on $30 car tabs because "nobody uses transit."
You're right that the "loop" need not happen and often doesn't in most circumstances but people are very persnickety about transportation and their deity-granted right to park their vehicle on a free street directly in front of their place of residence.
Edit: look at Seoul or Tokyo, with some of the best subway systems in the world, maybe the best. People still drive cars.
https://en.wikipedia.org/wiki/Orange_Line_(MBTA)#Rolling_sto....
Boston's T (1897) is just a year younger than Budapest's Metro.