Being a post-doc for most of your career and get a faculty job later; how likely is it?
What does "most" mean? Literally more than half? In usual circumstances it's highly unlikely. Let's say you start working on your PhD at the age of 25 and retire at 65, just to have nice round numbers. That's a 40-years long academic career. Now half of it would be 20 years of postdoc.

Out of all the people I've met in my academic field, math, I do not know one single person who has spent this long in postdocs. Off the top of my head the highest must be around 10 years, and the people in question had almost given up any dream of landing a permanent position by the end of it. Take it as you will.

I guess it can technically be "possible" for it to happen, in the sense that there is not some kind of physical or legal impossibility. But is it going to happen? I doubt it. Postdocs are hired for their promise of working well while they're at the institution, and justified or not, someone who's spent 10+ years in postdocs will be considered an underachiever in the eyes of many.