There actually was a little rebuilding, but only in the very last season, which was like twenty episodes. The season before that was about them searching for the treasures of Thundera, which actually is kind of like the new show.
I blame Nostalgia Filter, as usual. People just remember what they want to about old shows. The first two season of Thunder Cats is, if anything, about survival, or at least I think that's sort of what they were going for. Like you described, I don't think it was executed well.
Watching the show every day (yes, it airs every day on Teletoon Retro) I can tell you that even then, you are giving the plot WAY more credits. 95% of the episodes, no matter the seasons, have the Thundercats doing nothing at all. They are just lounging or dicking around in their fortress. Only Wilykit and Wilykat actually do things, and that's mostly get in trouble. Only reason they ever get out of the damn fortress is because the villains make them.
The survival/treasure hunting premise dies by the third episode when the Birbils build them their fortress.