The real reason is because they needed the Army of the Dead to get past a particular problem, but keeping them around to finish off Sauron would've made it way too easy (as you said), so they had to be released in order to keep up the dramatic tension. It wasn't really explained in the movie, and if there was an explanation in the book, it didn't stick with me. I think you're basically supposed to not think about that. There are a number of major and minor conflicts along the way to The Big One at the End, and if you think about it, The Big One at the End isn't really the big one anyway. Once the ring is destroyed, everything pretty much falls apart and The Good Guys don't really have to do anything but stand there and watch it all crumble.
But back to your point. Yeah, folks on the Internet love to pick apart every little detail. It's amazing how many people say things like "Overall, I loved it and found it very entertaining, but here is my list of 117 things that I found wrong with it".
In the LOTR book, the Army Of The Dead doesn't show up at Pelennor Fields, they only defeated the Corsairs (the guys in the ships) off page and allowed Aragorn too take those ships with a bunch of men from the rest of Gondor to Pelennor fields. So in the books the dead weren't really shown to be as ridiculously overpowered so it wouldn't have been as much of an issue why they didn't keep them. In the film though if they were going to show the recruiting of the Army of the Dead, it makes more sense to show them turn the tide at the big battle rather than just to take some ships (which wasn't even shown in the theatrical version) and spend time explaining that Aragorn found some more men to come and join the battle. But yeah, that does mean that we have to watch Aragorn get rid of them right after it's shown they can basically defeat Sauron's entire army. At least it was
lampshaded by Gimli a bit.
I would take a slightly different stance about the "nitpicking" thing, rather than it just being a case of there being less of it "then" vs. "now" being why, for example, LOTR avoided it. It may have got even more common now with social media and more people using the internet, but the same thing happened as long as the internet has been around (and before, surely, but I think the internet really made the difference as before then there wasn't really a good way or purpose for people who
dislike stuff to communicate about it). How many times have we heard about the eagles from LOTR for example? But despite things like that being widely pointed out as a "plot hole", that hasn't ruined people's appreciation for Lord Of The Rings.
The thing is, there will always be things to criticise and pick apart about any movie, but imo people are idiots if they thing those are the things that make a movie good. And that's where I think a lot of people go wrong criticising the prequels - they nitpick "plotholes" or individual silly events or designs that are supposed to be just self-evidently stupid... but the fact is similar criticisms can be made about things in the Original Trilogy or The Force Awakens. (For me, the fact that the Millennium Falcon is just sitting there unguarded in essentially working order, when it is driven home to the audience that people on the planet are poor, live in crappy conditions, and even make a living scavenging for parts, was a particularly ridiculous moment). But the fact is, where those films succeeded and the prequels didn't was on a more fundamental, "Filmmaking 101" level, not in having a story that makes perfect sense and no small elements to criticise. They were more competent films that engaged with the audience and provided an enjoyable experience, and that's why more people like them than the prequels - and it's why when people point out the problems with, say, The Force Awakens, more people try to explain it away or just say "I don't care", while when people do the same thing with the prequels more people say "Haha yes, that's so stupid".
That's why (and I know I have mentioned this several times) I like the Plinkett reviews of the prequels so much. Yes, they do just openly mock some of the designs or nitpick individual scenes that would be given a pass by most if they were in another film (though at least they do it in a unique and humorous way), but they also point out the deeper problems with the movies that made people not connect with them. It's the "Who is the protagonist of The Phantom Menace?" or "Can you describe any character without saying their job or what they wear?", rather than the "That plan doesn't make too much sense when you think about it" or "That was a stupid line about sand". Lots of people might not have even noticed that was what was wrong with it (... but their brain did) and so that's why they gravitate towards "plotholes" and "nitpicks" to explain it, even while giving similar things a pass in the OT or TFA.
For me, I found The Force Awakens enjoyable, and I look forward to watching it again when it's released on Blu-ray... I think it has problems but they were papered over easily because I was enjoying the ride. I also find it hard to take the story too seriously for some reason; it felt like a lot of what happened was very much just "this would be cool if it happened now" rather than coming naturally from the plot. I know all films and stories are like that to some extent, and I may have been affected by my outside knowledge, but for The Force Awakens it felt very transparent at times. That's why I'm not really interested in dissecting the storyline too much or trying to predict for the future.
I also think that the new trilogy(?), and perhaps even the retroactive reception of The Force Awakens, will depend more on the next film. I think people were very happy to just see a competently made enjoyable Star Wars film that felt more like the old ones after a lot of people were soured by the prequels... but once we get saturated with Star Wars stuff again I don't think people will be as forgiving.