It is probably good enough, but slightly more inconvenient considering how the eggs are prepared. It is pretty easy to slip an egg from a plate into a frying pan - some folks do this as standard practice. I was never sure of the origins until now.

If you are boiling, you are drawing some water anyway. It isn't a big deal at that point to have test water and add it into the pot when you are done.

Yep, that's the reason. Both tests would work fine but it's a matter of convenience.