“Why can’t a girl broaden her search and look for the sincere boy who is not interested in sitting and learning but wants to none the less build a frum home”.
There are many who do!!!
I know many nice girls who are eager to marry working boys, either college educated or not, and in the non-Chassidish world, there are many more girls than guys. The problem is similar even with non-learning guys.
Thats not the solution at all. Its a numbers problem.