Most European cities that shifted away from car traffic did exactly that. First they improved public transport and encouraged any other alternatives like bicycles. They invested in that infrastructure until it was ready to take over. Then they started to slowly "push" people away from cars by turning some streets or city centers into pedestrian zones.

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.

It's not a fake conundrum in political systems, especially when--as so often happens--road projects sail through the legislature with nary a peep but public transit spending has to be voted on (often more than once) by the people in the region or, sometimes, statewide. European countries often don't have these barriers or at least have a political and government legacy where the people see the investments as worth it. That's not a situation we often enjoy in the States, some reasons cultural and some self-inflicted.

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.

Some political systems make even the best solutions "a loop".