How much foam do you end up with? I usually don't rinse out the toothpaste after, but I don't end up with a foaming mouth after. I use about a pea size amount (as recommended on the packaging) and it's not super sudsy when I'm finished. Wipe my face and done.
I'm confused - what food bits? Do you have detectable food bits left over after brushing or is it an impression that there must be food still left over?
At least for me, I rinse out my mouth before I brush, so I don't expect to have detectable gunk left over. I also use a tongue scraper after, so I'm usually feeling pretty clean when I'm done.
Well both, stuff between the teeth that the brush doesn't get (I guess that's why you'd floss after brushing, but also with foam in your mouth?), and also just food microparticles that would go away when rinsing after brushing generally.
I suppose it helps to floss before brushing (as recommended) but for me personally the stray particle isn't something I've worried about. In my mind, the added benefit of retaining the fluoride longer outweighs the downsides of microparticles of food.
Honestly, the timing of flossing is the least important thing about it, considering most people are averse to even doing it. The payoff with flossing before brushing is that any gunk that gets brought out and left over after rinsing gets scrubbed away during brushing.