Again, this is speaking from personal experience and that of others I played with who were not in raiding guilds.
I remember having a hell of a time running the Netherstorm dungeons.
The player base was much less inclusive during TBC. If you were a casual not in a raiding guild it was difficult to find a group.
You weren't required to skip anything unless you were focused on the latest gear rather than playing content (I never cared about gear as much as the typical hardcore player). I played Ulduar after TOC because I was unsubbed at it's release and didn't care that there was no useful gear. 'Whatever level' refers to raiding I suppose. There was always something to do as I remember, and most of it remained relevant for play if not for gear (even as the dungeons got easier they were still fun).
Skipping content isn't required. It was still there and fun if not challenging for a hardcore player, who had the latest raid tier. My guild was happy to not be realm first when we got our rusted drakes. It didn't matter.