Why do Vietnamese dishes feature cut-up meat with the bone in?
Yes, those bones make a huge difference for flavor. If you just cook meat in water, you won't have anywhere near the rich meatiness that you get from a good bone broth.

Sure, you could get similar flavor by deboning the meat, then cooking with the bones and removing them before serving. But that's definitely more work, and in some cases it's pretty much impossible. (Want to try deboning a chicken neck?) Note that cutting through bones is not actually that hard; a sharp cleaver goes through a lot. It's one simple action, easier than deboning even for simple cuts of meat.

As for eating, you can just put the whole piece of meat (with the bone) in your mouth, then spit it out once you've gotten all the meat off. It's a lot easier than trying to hold onto the bone and bite it all off. That may not be common etiquette in Western cultures, but with cuisines that serve all kinds of food with small bones in it, I believe it's pretty normal.

In the end, there's of course still room for personal preference. Pieces of bone-in meat is easy for the cook (cleavers go through bones pretty well), and may or may not be pleasant for the eaters. If you don't like it, don't cook that way, just make a good bone broth instead. But it doesn't ruin the dish for everyone, and it's possible that if you just eat bone-in meat for a while you'll get used to it.