Perhaps break the two apart with the "well rounded" core being one degree (Associate of General Studies) and the major subjects another degree (Associate of [subject]). If you earn both, they get bundled into a Bachelor of [subject] degree. Employers could decide for themselves if they want to hire someone with just the technical skills and assume that the well-rounded part would either happen through socialization or not be relevant. I've found many of the university core classes I had to take for my degree to be useful in life but not necessarily useful for the workplace. Some, such as English composition, were useful in both.
“ Employers could decide for themselves if they want to hire someone with just the technical skills and assume that the well-rounded part would either happen through socialization or not be relevant.”
While not entirely crazy, isn’t part of the assumption of being well rounded that it helps you own your own career? Like it seems weird to me to externalize this as if you have no power in it. I study things that aren’t technical because it makes me a better functioning person/employee.
College shouldn’t just be about getting a job, it should be laying the foundation that makes you a better worker 20 years down the road.