Hi Gauv, when I look back at my average speeds more or less for pretty much all of my touring experience going back decades, is pretty much in the 16kph or 10mph range.
I can't really see getting that average a lot higher because 1- I'm just getting older and need to take care of my body , and 2- this really seems for me the right amount of speed and enjoying the experience -- but with the caveat that I accept that I am a pretty average rider and that is just what I am and thats okay.

I've always been surprised over the years how much more effort it takes to get an average speed up. Sure, I've had lightly loaded days with not a lot of climbing and or favourable tailwinds where I go faster, but all in all, I just don't train that hard and realize that my average speed is what it is.

For doing non stop days, I can only speak for myself, but I get tired of that. I can also get run down and have developed a cold or sore throat from not taking a break. I also just like the rhythm of taking a rest day, recuperating a bit, going over the bike and cleaning it well, checking things, that sort of thing, or simply walking around a town for a change of pace, not being rushed etc etc

as to your question about training, I do agree that doing indoor training work does help a lot. I've never done hours and hours of it, but it does get the legs ready to an extent.
cheers