Does catch rare drop when you are level 30+?

Seems that way to me.

Yup the common Pokémon are a lot harder as the level increases. I would still keep ultras for the very rares or high cp semi rares... the starter event killed my ultra stash and it sucks building it back up. If a common or semi common Pokémon flees me now (mostly just using normal ball, no razz) I shake it off knowing I'm saving the other balls for something better.

Yea this is definitely the case. I am level 29 and when a Weedle pops out of a ball 3 times, I just want to scream “Nobody even wants you, you are lucky I am even doing you the honor of hitting you in the head with a ball”

Probably just observational bias - I'm level 32, really hate it when I nail a mid-level grinder (think 150 CP weedle) with great throw after great throw - when I finally capture him and check appraisal seems like it's always "your Pokemon sucks". I know it's random but give me a break! I've wondered if it would make sense for high IV's to lower the catch rate... (as long as not too large of a difference).

I think it's just the greater spawn of high cp mons that you get as you climb the levels that makes it seem harder. Sometimes I'll waste balls on the stubborn blighters, other times I have the sense to walk away...

Catch rate in influenced by CPM, which depends on the pokemo's level, since in turn, the higher your level is, the higher the level of pokemon you can encounter, that means pokemon DO get harder to catch when THEY are higher level, your level doesn't factor into this directly.
https://pokemongo.gamepress.gg/guct-curveballs
https://pokemongo.gamepress.gg/guct-berry-throw-bonus-multipliers
https://pokemongo.gamepress.gg/guct-medals

According to the formula, you should stack as many multipliers as posible, that way, each multiplier is "worth" more.

I'm only L27 and have thrown several great balls at generic cannon fodder and I get to thinking... oooo a ditto... but instead i get the "gotcha".

Speaking of which... I haven't seen a ditto since the 1st week or two after its release. Anyone else still finding them?

As you run across higher level pokemon they are definitely harder to catch. It sucks trying to catch a level 30 pidgey or rat etc.

I do try to catch everything but I will pass on some of these guys at times as I just don't feel like wasting 10 balls trying to catch a rat.

You need to wait until the circle is small. A "nice" throw isn't actually good.