If the Diffys loved the 21st century so much, why didn't they stay, especially considering the relationship between Phil and Keely? The answer lies in the penultimate episode: they came dangerously close to creating a time paradox by interacting with one of their ancestors. Much as they wanted to stay, that incident convinced them that staying wasn't safe.
Actually, it was the new restrictions on time travel that made it impossible for them to stay. The "Because of the Diffy's Law" that Lloyd finds out about when he takes the time machine for a test run in the last episode.
The "Thanks to the Diffies" law was preventing them from returning to the 21st century. It never said anything about them staying, just that once they went to the future they were never allowed to go back to the past.
It's possible that the law was made because of said paradox. Unless Keely messed up that much by knowing.