I've hiked mountains and volcanoes, and hiked national trails for months at a time in Japan, portugal, Italy, and i wouldn't say it's more rewarding to climb mountains.
you sound like you're leaning toward walking anyway, and I personally love walking because you're going slow enough and it's comfortable enough that you can appreciate everything going on around you at all times, rather than only at the peak or the summit or particular lookout points.
there are far less things to worry about, oxygen, dehydration, joint sprains, and you can enjoy the extended stroll.
I think the body conditions very quickly, and you probably would be able to hack a month in the mountains, but it's also very healthy to walk, and I find it much more enjoyable as an overall long-term process.