Granblue fantasy

How much sense does it make to assemble a party based on a single element?

So much that it's the only viable option, at least until mid-to-high tiers. The vast majority of weapon skills buff a specific element.
Silver ones can be used. Well, some can, some can't. I don't recommend bronze ones.
You seem to have a decent light party with Soldafon, De La Fiy, and Saria. Well, you should replace the last one later with someone else who is light.
In water, there's Silva, which is very cool. Take Catalina and Liliel there and get a group that's no worse than the light one. More precisely, it will be clearly better, but the downside (for you) will be that it won't have Soldafon.
Air: Fina is so-so, but Carmelina seems quite good. I would take Hazen as the third, but that card is also geared towards Vira, and Vira is of a different element.

By the way, I also like Barava.