I don't know that putting a loan officer or a lender approval panel into the mix of a college kid struggling to choose a major is a great idea.
And the problem you pose is easily solvable. They have to re-apply for loans every school year. Maybe pretty much everyone gets funding freshman year before they declare, but when they re-apply for sophomore year their major is taken into account. If you switch majors mid-year, then when you re-apply the following year, you get evaluated. Or if you received funding for a given year, you are not allowed to switch your major during that year.
EDIT: It's really not all that different than home loans being determined by income, credit history, etc. If you are going to ask for a $500k home loan, you better have the income to pay it back. If you are going to ask for a $100k student loan, you better have the projected/expected future income to pay it back.
What reasonable assurance do I have that my kid won't get denied for his senior year, thus being $100K+ in debt and without a degree? (which is probably worse than the current federally subsidized system)
What assurance do I have that the terms won't get dramatically worse by a private lender for the junior and senior year and for this to be driven by "Now I've got you by the shorties" rather than by "basket weaving is not a lucrative career"?
What effect does that have on smart students of middle-income families who don't have the resources to pay for college without loans, yet make too much to get sufficient need-based grant money?
Part of the problem is that resource extraction and redirection activities are drastically overvalued, while activities that generate lasting social value are drastically under-rewarded.
You can't expect markets to correct this, because markets are part of the resource extraction/redirection system, and will always overvalue themselves and undervalue competing social mechanisms.