Gut bacteria have many functions, and there are likely more out there to be discovered than we know about currently. One of the functions that I find interesting is that bacteria help to synthesize vitamin K, which is required by the liver to build proteins that allow blood to clot. Neonates do not have the gut flora to synthesize vitamin K at birth, which is why they get a vitamin K shot after delivery.
Normal gut bacteria also coat the GI tract, preventing pathogenic bacteria from sticking to the surface of the intestines. This is part of the reason babies under 1 should not eat raw honey (which has C. botulinum spores that can stick to the intestines and produce botulinum toxin), while older kids and adults have no trouble with it.
Along the same lines, a hot (though, admittedly disgusting) area of research in medicine now is fecal transplant for people with a particularly aggressive form of colitis. I believe that the research on glut flora transplantation is also being expanded to weight loss, but I'm not very familiar with the studies.
Glad you've not noticed a change, that is probably good right! I think the Gut microbiome extends further than just the large intestine, you've probably got some bugs hiding out somewhere in the system :) https://www.newscientist.com/round-up/microbiome/
You still have gut bacteria in the small intestine, and they're probably as important as the ones in the large intestine. I can guarantee you that without both the small and the large intestine, you do notice a difference (but unfortunately for reasons more serious than just not having the bacteria). Glad you're adapting well to living without the large intestine!
I would presume we need them because every healthy human being has them after one to two years of age.
We also know that antibiotics that kill gut flora lead to health/digestion issues until the gut flora is replenished.
It doesn't take nearly as many why questions to get to a "we don't know" answer with biology versus physics. There's lots of stuff about biology we can observe but do not understand the why as well as we understand something like the physics behind a microprocessor.
Yes, gut bacteria are very important, they serve many functions, not all of which are understood fully. For example, it is estimated that 90 percent of the body's serotonin is produced in the gut, it’s the chemical that helps with sleeping, eating, and digesting. If you want to read more, have a look on PubMed for articles relating to 'Gut Microbiome' like this, https://www.ncbi.nlm.nih.gov/pubmed/?term=gut+microbiome
