My experience the only time you really need to be sure you've got a well rounded and versatile team is in certain Incarnate Trials, and MO*TF runs.
However, I will also agree I've seen teams that should not have been running +4 wanting it at +4 and wiping constantly because the team they had was not capable of handling it. I'm not sure how much that is about AT choices though, or just the characters in the party not being strong enough yet.
Yeeaaah. While I mostly agree with the spirit of the original post, some of the assertions are not really on point.
DPS doesn't just refer to damage, it refers to characters that excel at putting out large amounts of damage in short amounts of time, such that you can overcome the regeneration or phases of especially tough enemies. DPS is not really required for a lot of content, but when it is, it is. What makes City of Heroes unique from most other MMOs isn't that 'everyone is DPS' because everyone is most certainly not even close to being that, but that if content is too hard you can turn down the difficulty. This works for a lot of content (radio and regular missions, not always task forces or trials).
Some of this stuff also just only applies to characters with full IO sets. Try taking a full team of 8 scrappers into the ITF +2 at level 35-50 with only basic IOs or SOs and they're almost certainly going to get floored by -def and spike damage from hard hitting enemies where even 75% resist isn't going to be enough. Likewise, take a team of 8 tanks or 8 controllers in and you'll get through 99% of the Task Force but it will take _so_ much longer, and both are going to have (different) issues with the AVs (not insurmountable ones, but a huge pain in the ass nonetheless).
The holy trinity is not so very holy in CoH, and for plenty of content you can turn the diff down and get by with suboptimal groupings, but anybody who says they haven't seen teams struggle with content where it wasn't pretty obvious that you needed a scrapper/blaster/etc for more damage or some support with +end for all the people struggling with endurance issues vs Freakshow, instead of whatever you have instead, is either lying to themselves or not paying very close attention.
You don't need to min-max your teams, but for the love of god consider the content you're facing when you're throwing out invites. If you're going to be fighting two AVs at once, at +2 or higher, and there are zero support sets on your team, shrugging it off because 'any team is viable' is almost certainly a disservice to your teammates and frustrating to boot.
There's really no need to lean so heavily against the trinity idea, just like there's no need to lean so heavily into it.
Also, please stop pushing this idea that Empathy isn't Healer. It has 9 powers, and more than half of them are directly involved in increasing your health from wherever it is towards full, whether it's by direct heal, resurrection, or super regeneration. Adrenaline Boost has more +end than +regen, but even if you don't count it as 6 of 9 there's 5 that are straight up heal/regen powers, 1 that's a mix, and all of 3 that aren't HP related. It's a healer set, full stop. People shouldn't skip those three powers, but it's absolutely a healer set. :p