Clay drove for BRM in 1973, so his spell at Ferrari wasn't uninterrupted. Given the machinations at Ferrari in the 70s, the spells tended to be short.
It was a very competitive time in F1 too - after Denny Hulme secured a driver's championship with Brabham in 1967 after Brabham's own success in '66, no team won back-to-back driver's championships until McLaren in 1984-86 with Lauda and Prost. So the top drivers tended to have a bit of mobility, chasing after the most competitive drives.
It wasn't until the Ford DFV started to become uncompetitive against newer engines, which happened just before those McLaren successes with the TAG-Porsche engine, that we really saw any team stay at the top for extended periods. Since then, however, it has become more the norm and we see some drivers do long spells at a single team. Even now though, I wouldn't say it was the norm.