Yes. If you want to be competetive, make sure you have 31 IV's in the two most important stats. The other stats should be 27+.
kind of going off of this, is there any way to determine IVs after you have already raised a Pokemon?
Nonsense.
If a pokemon is supposed to reach a certain speed, you should definitely aim for a 31 speed IV. Similarly, if a leftovers threshold can only be reached with a high IV, aim for that. Everything else is fine if they are in the highest quartile (24+).
I'd like to point out that IV and trait breeding isn't very difficult. You need to average 100 eggs to get a Jolly Gible with 31 IV in Attack AND Speed. I don't know if you find 100 eggs tedious, but rest assured that 100 eggs isn't too much.
Have you ever bred Gible? It takes an eternity (10,240 steps without Magma Armor, 5,120 with)... even with a Slugma, add on the part that L1 eggs require you to level up most of your newbies to really check their IVs... you can either save->use Rare Candies->reset or use Victory Road, but either way it's pretty annoying. With something like Magikarp, sure, 100 eggs takes a day, but with Gible (or Larvitar or Dratini or Bagon), it takes probably a couple days...
Breeding for IVs isn't that tedious tbh.
Legendaries take a bit more work... Took me about 50 tries to SR for a Modest 30/20/22/29/29/24 Dialga (Speed Last) with my Synchronizer.