If I'm being completely honest, I think when it comes to fighting game crossovers, characters are important as both characters and functions rather than just one or the other. If I had to lean on one side, I'd say focusing on function is more important from a gameplay standpoint, but the actual character of the characters is also important.
If you have a huge roster of recognizable characters but not one grappler, people who like playing grapplers are going to be rather disappointed.
At the same time, though, not only is having well-liked characters good for marketing, it opens up the floor to means of representing more playstyles and functions. For instance, continuing with the grappler examples, if I were to add Zangeif to Smash, not only would I be adding a character that Street Fighter fans would enjoy, but also those who like playing grapplers. Adding a character (if designed well) appeal to both the fans of the character and fans of the archetype they embody.
On the strictly character side of things, personality is also a big factor. For example, Fox and Pichu are both rushdown characters, but while one's a confident mercenary, one's a playful, clumsy electric mouse. Characters allow you to cover a lot of archetypes with different personalities, which allow players to find a fighter with both functions and aesthetics they enjoy.
In short, while designing your roster around functions is important, it's also important that the characters you choose can cover a lot of different personalities and aesthetics to suit as many players as possible, both casuals who want to beat up Sephiroth as Kirby and competitive players who want options when it comes to their favorite archetypes.
