Although I like your economic reasoning, I don't think the additional cost of non-law students really affects the decision-making process. HR don't care and often the partners interviewing you don't even know your background.
If you don't have any work experience I can thoroughly recommend going the 'informal route'. As well as applying for open days/vac schemes, email partners to ask for informal, unpaid internships. They like it because it shows entrepreneurial flair, ambition and boldness. Plus, you get to see the firm's true colours rather than some fancy masquerade that they normally show budding applicants. Plus plus, you don't have to compete with loads of other budding applicants. Plus plus plus, emails to partners are a much more economic use of your time: you can look up individuals' CVs online and find someone who will be sympathetic to your background to maximise your chances of success.