I just found out how my girlfriend makes pasta: She uses a (non-stick) frying pan to boil the water. I told her she should use a cooking pan. When she asked why I did not have a response. After some internet searching I still have no plausible arguments, it just seems absurd.
If you're making a small enough quantity of pasta for it to totally fit in the pan like that, it's fine. The idea that you need several quarts of water, several times the volume of the pasta, is a bit of a myth.
All you really need is enough water so that once the pasta is cooked and fully expanded, it's still covered. So depending on your appetite and the size of the pan, this might work for one or two servings, but not a full meal for many people.
The main concerns I'd have with cooking in a frying pan are:
- since it's a broader surface, you'll lose water to evaporation more quickly, and risk ending up with too little water even if you started with enough - you might need to watch it more carefully than a big pot
- the sides aren't tall enough to contain it for long if it starts to foam and boil over - again, you might need to watch carefully
- it won't be able to hold enough to cook a very large quantity of pasta
If you avoid all those, I don't really see the problem!