Don't despair, my friend. Many shows have character leads.
FYI, there are 3 main 'types' in musical theatre. For females they are Ingenue, Character, and Leading Lady. There are certainly crossovers and people who do both or all three well, but just to kinda give you some examples...
Ingenue - the romantic lead. Usually beautiful, with a (in the old days, not sure how it'd be categorized for more modern shows) more soprano lyrical voice. Think R&H Cinderella, Guenevere in Camelot, Sarah Brown in Guys and Dolls, Eileen in Wonderful Town...
Character - I think you know this one already, lol.
Leading Lady - Ethel Merman was always used as the perfect example of this. She's definitely not ingenue, but if you were to try to categorize her as 'character'...it just seems off; you can't picutre her doing character type stuff well. Despite either of those, she can still carry a show - roles for Leading Lady types are things like Mama Rose, Norma Desmond perhaps, the lead woman in The Cherry Orchard, Antigone, Marie Christine would maybe fall into that category, Ruth in Wonderful Town, maybe Elphaba in Wicked...
I dunno if that helps or not, but jsut know that you have a third option besides just ingenue or character, adn that there are plenty of great roles for that type as well - in fact, in my opinion those are sometimes the best roles; they seem to require more acting chops and often more deep with a better journey...again, just my opinion though.
If I show you the darkness I hold inside, will you bring me to light?