Like you, I have good teeth (never had a filling) and on average have visited the dentist about once every 10 years.
Like you I also used to never be able to get floss in between my teeth, but after a dental checkup some years back the dentist cleared all the plaque buildup and from then on getting the floss between my teeth was no problem, and I've been flossing regularly since.
Once the plaque builds up and hardens, it's very difficult to break it up with just floss and you'll have difficulty getting floss in.
For what it's worth, my teeth definitely feel cleaner after flossing, and if I miss a couple of days they start to feel dirty.