For what reason is Not Quite Dr. Cliché's Underwater Lab so infamous?

Is it because it keeps being misused, or it's just used way too much?
Without enemies and the like, would a screen like this:

and a screen like this:

both be equally groan-worthy?

The tileset was used a lot, probably more than any other thanks to being the default selection when you create a new level in the editor. (In fact, your first example is also using the default gradient selection.) People got tired of seeing the same old graphics with the same old songs.

At this point in time you can safely use it without many complaints. There aren't many levels being released these days, so any well made level will be welcome. Some people even feel nostalgic over levels that remind them of the early days of Knytt Stories.

Ego is right, I think. Back when there were many more people playing this game, inexperienced players would use the default tileset and ambience/music/gradients and produced poor-quality levels, so the default settings became negatively associated with. Personally I don't think either of the screens you showed as an example look terrible.