What makes Claw's secrets "the best parts of the game"? If it's just that they're harder, then doesn't it make sense that they're hard to get to?

It is the way those parts are designed, common obstacles are used in more creative and clever ways, you can't beat those parts at first try, it requires more skill and planning and even some basic puzzle solving. It is a more complex design that is usually seen in later levels of games, where everything you learned so far is put to a test, like a epic hard battle in a shooter or
more complex puzzles in a puzzle game near the end. Now imagine if those were all secrets in those games and you missed them. Last few levels ARE very hard, but the design approach is more basic than in those secret areas.

I dislike secret areas you have to backtrack to. In the vein of "Here is 37 things you can't do yet that have goodies behind them. Go through 80% of the game to gather all the necessary powers/equipment and come back later."

Talk about a time-wasting mechanic...

That's exactly what I was thinking. Always had a great laugh playing those (despite it being quite hard).

Was that hidden? I remember seeing it when I played the game.

Good question, it's been a while for me, but I remember it being a hidden easter egg. Could be wrong though.

If I'm playing a game that I suspect or does have a reputation of having secret areas, close to the end boss I'll check on a walkthru if I found all secrets by myself. If I did not find everything and I'm enjoying the game a lot I'll leave them for a second playthrough. If I'm enjoying it but not enough to want to play it all again I'll backtrack right away to 100% it.
And if 'm not enjoying it I'll just play something else of course.

On the other hand this means that undiscovered secrets that are not accessible anymore do piss me off unless I'm already up for a second playthrough. This includes secret areas and any other permanently missable content.

You just described possibly my favorite genre: Metroidvanias...