Bahamontes and Poblet were exact contemporaries (they were born in 1928). I recall at least two great cyclists from Spain older than Poblet and Bahamontes.
Julián Berrendero (b.1912) was the KOM in the 1936 Tour and won the Vuelta in 1941 and 1942. Sadly, most of his career was during the time when Spain first, and then the rest of Europe, were in war.
Jesús Loroño (b.1926) was also KOM in the 1953 Tour and winner of the 1957 Vuelta.
So the tradition of Spanish climbers and stage race contenders is older than Bahamontes. And the interest of media, sponsors and public in stage races and GC contenders is massive compared to that of 1 day races.
Poblet is a living legend, but it was a singularity in the Spanish peloton. Guys like Freire and Flecha are also a singularity. All of them have spent most of their careers in non-Spanish teams even if they started in the pro-peloton at a time when Spanish sponsors for competitive teams were not as hard to find as today.
EDIT: First Spanish cyclist who won the TDF KOM was Vicente Trueba, in 1933. He finished 6th in the GC. Spanish climbers were around when Miguel Poblet was just 5
