I agree with the point that doing a degree just as a fall back is a bad idea. It is expensive, extremely time consuming and very hard work if the degree is worth anything at all. I did an electronic engineering degree. It was very much a second choice in life compared to flying but definitely never a fall back. Back then I simply could not get into a cadet program and there was no way I could see I could afford to go the self-improver or integrated route. As it turned out engineering was a good choice. It has served me well as a challenging and interesting profession and once over the first few years after college, paid me pretty well too.
Years later personal and financial circumstances changed such that I arrived at a point recently where I re-examined flying as a career option. Following aptitude and medical tests, I found it was an option and I could now afford it. So soon I will be leaving engineering and hopefully in about 2 years time I will make it to the RHS (of something/anything!) as a paid professional pilot. If for whatever reason I don't make it I have a fall back. My fall back is there not by design, it just worked out that way and I really do not want to have to use it.Short term it's not a particularly useful one either as the nature of my type of engineering means committing to a design project for at least 6 months but more usually up to 2 years. I can step out of electronic engineering for a good number of years without getting out of date, believe it or not it hasn't changed that much in the last 10 years. However stepping back in and out on a week or so's notice is simply not an option. So if I do get to the stage where I have an fATPL and am in that uphill struggle to land that first job, I must consider options other than engineering to earn a living.
I think WWW is about right when it comes to picking a suitable jobs to fall back on if that is all that you want that job for - ideally find something like an apprenticeship you are interested in and pays well enough for those flying hours - mechanic, electrician, carpenter, whatever and something you can pick up or drop at short notice.
As Scroggs has said before, airlines are probably not looking for degrees, they are looking for good pilots. Having a fall back is your choice and your responsibility. I can't imagine airlines really care if you have one or not. If I was doing the hiring and firing I know I wouldn't.