Yeah, it's just tradition at this point, though I feel like native speakers really try to oversell its usefulness when someone questions if the opening signs are necessary. People act like they routinely need to read text written like the Cartas de relación out loud, and thus, need the additional warning lest they get lost in the long, multi-clause sentences. Like, I could understand if you had to read something like

Y después acá, por no haber oportunidad, así por falta de navíos y estar yo ocupado en la conquista y pacificación de esta tierra, como por no haber sabido de la dicha nao y procuradores, no he tornado a relatar a vuestra majestad lo que después se ha hecho; de que Dios sabe la pena que he tenido. Porque he deseado que vuestra alteza supiese las cosas de esta tierra, que son tantas y tales que, como ya en la otra relación escribí se puede intitular de nuevo emperador de ella, y con título y no menos mérito que el de Alemaña, que por la gracia de Dios vuestra sacra majestad posee. Y porque querer de todas las cosas de estas partes y nuevos reinos de vuestra alteza decir todas las particularidades y cosas que en ellas hay y decir se debían, sería casi proceder a infinito.

out loud on a regular basis, but even contemporary literary Spanish doesn't tend to have nearly the same amount of sentences that just go one for half a page, much less the sort of stuff people would write to each other normally.

As you've mentioned, other syntactically similar languages do just fine without them, even including other Romance languages spoken in various regions of Spain. The only exception I'm aware of is Asturianu, which apparently also uses them, though apparently they're optionally allowed in Galego Real Academia Galega. On page 38 of the PDF, it says they're entirely optional if you want to facilitate reading by including them.