This article looks at
closing roads that are more trouble than they're worth.
"When it's in an unstable location" is a good reason to close a road. Cut the worst problems, the most expensive drains on the budget, before cutting things that are sort of working.
However, I would add "after you establish a core" in regards to timing. Suburban sprawl is unsustainable, so one way to deal with that is to concentrate growth around core areas and let the sprawl between them dwindle. This will be a great deal easier if the cores are built up
first. The article mentions that the troubled road connects clusters of suburbs. In such a situation, look at why people are crossing between them. Likely reasons include jobs, schools, and shopping. Make sure each area has those things, and the connecting road will become much less important.
Look at suburbs. Most of them have some kind of activity center either near the middle or along the edges, remnants of the older (and much more functional) traditional neighborhood design. If you build up those areas so they contain most of what people need, that undoes a lot of the
damage that suburbs did by segregating activities.