I really don’t like the example of “monter en haut”. Certain verbs, like “monter” can have very different meanings without the noun.
Monter en haut: to go up (not specifically stairs, contextually maybe, could just as well be an elevator or a tree house ladder for example)
Monter a cheval: to get on a horses back
Monter un meuble: to assemble furniture (think ikea)
The noun here is not irritating, it’s essential.