Powering up mediocre mons because they are shiny?

Absol, and keep Aerodactyl as a trophy.

I don't and I wouldn't

If you want to power them up just to show off in gyms, maybe just take them up to level 30.

Reason for doing it:
* Shiny Pokemon are always nice and if their IVs are great, then it's a nice little trophy to have.
* Neither Aerodactyl or Absol are completely useless and if you really need one for a squad, then I guess there are worse(?) Pokemon out there.
* We are most likely going to get another bonus Stardust event later this summer. So you will be able to get some more.

Reason for NOT doing it:
* Neither Aerodactyl or Absol are great Pokemon. I am sure you can find a better one to put in your Psycho-raid squad.
* Shiny is nice, but it doesn't make them better.
* Trading is coming and will cost Stardust.
* Gen4 will be out in a few months (probably) and from what I can tell there will be some rather interesting Pokemon coming that might be worth spending some dust on.

Might be some more points that I can't think of at this moment (it's past two in the morning and I'm tired).

Also, I am notoriously stingy when it comes to Stardust (I haven't spent any in like seven months), so I might not be the most unbiased person to comment on how to spend Stardust ;)

Personally considering I love Absol and actually find useful, I don’t need it at all but I still put in my gengar Alakazam squads for unique 6 I would without hesitation max out that shiny Absol!

I caught a low-leveled shiny Charmander that was A-D-S 14-0-1 or something. Got that BB and powered it up to level 30 for fun.

I powered up a Pidgeot that was my very first 100% just because I was so proud of it at the time. Hopefully I can give him the Mega Pidgeot treatment someday soon

I've made it a point to power up at least one shiny every Community Day. My Ampharos is only 60%, my Charizard is 64%, and my Dragonite and Tyranitar are 77%. I was lucky to get an 87% shiny Venusaur.

No regrets so far, their CP is only 100 lower than a 90+% IV at most. Makes little difference, especially if I place them in gyms.

I'm currently working on powering up a shiny Shellder that I caught a few days ago. It's 14/15/14 95% (my only 90+% shiny up until now) so it's definitely worth it.

Edit: Just realised that I misread your question. Do power up your Absol, since it's usable in certain matchups. I wouldn't bother with Aerodactyl.

It's about the bond between you and the Pokémon

I've been slowly powering up non-relevant 100s (including an Aerodactyl) just because. Like you i have most meta- relevant high level guys so I'm spending dust on other fun projects to keep the game amusing.