The 'oldspace' industry was so absolutely antagonistic and dismissive of reusable rocketry, there's no doubt in my mind that it would not have been pursued. The whole idea was associated with the Shuttle, widely considered to be an albatross for NASA.
Those young engineers you mention would have vanishingly little influence on development of any new rocket program in a deeply bureaucratic, ossified system. Who even are these 'other' rocket companies developing rockets? ULA is the product of government contractors simply supporting Atlas and Delta. Until Bruno, there was no real possibility of a new rocket program. There's Ariane, Roscosmos, China, and India, so mostly impossible for US citizens. It's very likely Ariane would not even be developing a new rocket if it wasn't for the specter of SpaceX.
The most important thing to understand is that rocket development wasn't progressing. It was excruciatingly stagnant, entirely dependent on the government to take the initiative, and subject to constant political muddling.
Musk created the environment and goals that let these engineers achieve incredible things. Without that environment, I don't see these engineers having the same accomplishments.
Unless you think that Musk is a once in a generation rocket engineering genius directly responsible for designing their reusable systems, it stands to reason that they would have been invented anyways (but probably more slowly).