But on the other hand the idea that a Bard doesn't get cheap music skills, and a Dancer can't dance better than a Wizard, does feel wierd.
That is because of the specific tags associated with the professions (which, once again, should not be named professions...). In fact, professions most often associated with a specific field of action and/or magic. In original RM, professions were linked to primary skills and available spells only. The "secondary" (or "flavour") skills were not included in the mix, and professions were adventuring stereotypes.
Which could have another, completely unrelated "real-life" stereotype added on top of them - you could be a magician-dancer, or a fighter-moneylender, and no one would bat an eye, because the real-life stereotype and the adventurer stereotype were unrelated.
Introduce secondary skills, but link them to professions, and you remove the flexibility, because you assume that stereotypes are in fact real-life occupations. Which, in addition, requires to create additional stereotypes (professions).
As it is, RM is less flexible than D&D as far as skills are concerned, which is somewhat surprising.
We've come from a "Bard" being called that because they are a semi spell user which specialises in information and mind-affecting skills, to a "Bard" being called that because they are a wandering minstrel that happens to have spells (because, you know, adventuring). Same name, but different impact.