What’s stopping a bachur from picking up a mikraos gedolos and start to learn nach in his spare time? This is what I did in mesivta instead of reading novels. Learning mishna berura isn’t a bad idea either. Are yeshiva bachurim so helpless now that they can only learn what is spoon fed? I think they are capable of their own extra limudim.
My grandfather was from the Mir Yeshiva. I’m told he would love to learn tanach when he came home from work. I’m pretty sure it was a lot more prevalent in the yeshivish crowd to be proficient in nach even though it wasn’t kavua.