How important are IVs in PvE anyway?

The difference is small but "adds up" if you use the specific Pokemon regularly. IV matters most when heavily investing scarce, important resources.

For example, gyms in my area are very competitive, so I have a few maxed Machamps and Blisseys. A 98% Blissey is only very slightly better than a 82% Blissey, but sometimes the 98% Blissey will earn one or two more coins (due to delaying the attacker long enough to feed another berry). Earning enough Chansey candy to max out a Blissey takes a long time, so I will definitely spend the 300+ candy on a 98% Chansey rather than a 82% Chansey. Likewise, a 98% Machamp may occasionally be a second faster than an 82% Machamp, or survive a charge move that an 82% Machamp would not. Considering how many battles my Machamps have fought, I am sure this has happened many times.

IVs are a little bit overrated. The difference between a 0% and 100% Pokemon is about 10% in overall effectiveness, so your 70-something Groudon isn't going to be far off someone's hundo.

In some communities, the competition is fierce and it can be an attitude of 100% or nothing. For others, it's merely another carrot to chase, like shinies.

Personally, if I'm going to use something regularly, something that I'll invest stardust and candy in, I want it to be the very best it can be. 100% is obviously ideal, but I'm generally content with 96%+. For more throwaway/niche applications, I'm happy to go with something lesser.

IV's mostly are important when it comes to reaching break point/bulk points, being able to deal one extra damage with a charge/fast move, or take one less damage each attack or survive another charge move is important and does add up, but there arent many cases where that leads to a massive preformance difference, the only ones I believe have a noticeable (not massive) preformance difference when it comes to IV's are glass counters or tank counters not reaking a bulk point for the glass coutners (think gengar v mewtwo unable to use a shadow ball before going down) or something like a tank counter tyranitar not reaching a breakpoint and dealing something like one less damage per bite, which is why people tend to put more emphasis on Attack IV (see all the 15 attack sticklers out there)

It doesnt always happen and I wouldn't say they are negligible, they certainly arent anything like a 0/0/0 MM metagross preforms the same as an aggron, the preformance is, while it does lag behind a perfect, not at all substantial enough to downgrade it as an attacker, movesets are the most important factor, as are stat distributions/base stats. I feel the IV preference for higher IV's can comedown to a few possible reasons

1) blatant elitism, theres a number of people who I know from both IRL and have seen online that only go for 96+, 15 atk mon when an 98% 14 atk has an almost identical, it not identical preformance, though this doesnt seem to be common

2) the more common on in my experience, as I myself am like this, is going for higher IV ones because they are better, while I have said IV differences are small, but for things like legendaries and pseudo legendaries, pokemon that are somewhat difficult to get large amounts of candy for, players tend to only go for the best of the best with them, as there are times break and bulk points can really matter. (Though there are players that evolve level 30+ wild catches of things like larvitar, bagon. dratini and beldum as they are at high level and do not need any input aside from evolution, its to save on cost even if the iv's arent good, they still are extremely powerful). Higher IV's do make a pokemon better than a lower IV variant, though not by a gap of if its not at least 91% it's preforming like aggron, the difference between a perfect and a 0% (as I call them imperfects) is only a couple percent, perfects are the best, but imperfects are still solid, I feel this one comes down to mostly players wanting to spend their candy thats hard to get on something they know wont get bested by a higher iv version and they'll always have it as one of the best of their species on their teams, even after about a year I still use my 96% DM dragontie form the CD

and 3) this is somewhat similar to the second, but a little different, its the practicality. As I said before Iv's have an impact, though not a large one in most cases, however the cases they do make an impact, ie hitting break and bulk points, are substantial. Back to the example with the tyranitar I said earlier, a tyranitar dealing one extra damage per bite it uses, given how long tyranitar lasts, that is a lot of bites. That extra one damage will add up. Adding that to reaching a bulk point and being able to survive longer by taking less damage (and thus being able to use even more bites) will also add up. Though these points are not hard set, like tyranitar must have 15/15/15 to reach every break/bulk point, they vary on match ups and moves, and most of the bulk and break points I have heard of aren't 15 IV's, from what i've seen most break and bulk points on most pokemon tend to be in the 11-14 range

For defense, iv's are irrelevant, a pokemon in a gym is almost never at max CP, and thus almost never has the 100% stats

TL;DR, Better iv's do mean the pokemon is better, but not by a lot, the lower iv variant is still great if the perfect is amazing. Movesets, base stats and type match ups are much more important.

Your 70-sumthin shiny will beform almost the same as someone's 100%, like my shiny 70% kyogore preforming almost the same as my 93%, the iv's matter little unless you're super competitive, sorry about the long explaination

I have hardly ever noted a difference. Only when doing solo raids with seconds to spare.

Many people do not seem to remember that base states (species), move set, level and, not at least, what you use it against, are what really matters. IV is just a thin layer of extra frosting on the top.