Thinking about it now, in a way I guess this might have been an experiment of sorts. In presentation, unlike Shadow Dragon and New Mystery, Shadows of Valentia probably is higher than any of the existing titles (battle animations redone and improved again, more detailed models, full voice acting for the main story). It also has casual mode, so the accessibility is there.
However, it lacks the avatar and shipping aspects of recent titles - there are supports, but they're very limited in number and romantic pairs are pre-defined. In a way, this basically weights how much presentation and accessibility count compared to those features. Although, this seems like a weird game to do a trial like that, considering how it's based on a game infamous for its map design and odd progression among the older fanbase, and they did nothing to fix that.
I think you're thinking a bit small scale actually. This might be easier to explain through the lens of Western games.
So, the four Western titles I listed (Gears of War: Judgement, God of War: Ascension, Batman: Arkham Origins, and Borderlands: The Pre-Sequel) actually all did a good job of maintaining the feature sets and production values of their previous entries, and all of them added new features too.
We can even look at a game like Arkham Origins on paper and see that it sounds pretty impressive. There's a whole new cast of villains. The map is twice as large Arkham City. It follows Batman's Year One storyline with what was largely considered notably better writing. It had a new multiplayer mode. The combat upgrades were well received. It seems to fit all the checkmarks. Despite all this, it didn't have any features that really captured people's imaginations, and after already playing two lengthy games of this formula, people didn't want what still felt like too similar an offering.
Arkham Knight's massive scale increase, shiny new graphics, and batmobile seemed like a far more compelling proposition to people, even if it was a shorter list of new features. (I also like the batmobile example here as it shows that features don't necessarily have to pan out to be good to seem conceptually exciting.) Warner Bros understands this, and the next Batman game makes major change-ups to the formula if rumors are to be believed.
We can also look at God of War: Ascension, which had no excitement, versus God of War 4, which actually has excitement. God of War: Ascension basically offered "Yep it's another God of War game." with a multiplayer mode that seemed like something you would try for a couple hours and never play again. God of War 4 tries to reinvent the entire series to modern day tastes with a new setting, art style, new narrative angle, and what appears to be a very heavily changed up gameplay experience and game structure.
Assassin's Creed is also a great example of lots of different potential outcomes based on what type of game you make.
The first game was conceptually ambitious, but really rough. However, people were very excited for conceptual ambition in the early part of the generous, and bought a zillion copies of the game despite its flaws.
The second game was a major budget increase over the first, and tried to really achieve everything all the first game's potential and respond to the critical feedback about it. It sold a zillion copies.
Assassin's Creed 2 was so good that people were willing to buy a game that was a marginal enhancement of it with a few new features. Brotherhood kept something like 70%+ of AC2's audience.
However, people were not especially willing to do that twice, and Revelations collapsed in comparison, especially in terms of average selling price.
Assassin's Creed 3 heavily changed up the formula and offered lots of ambition, even if people debate if they liked it more than Assassin's Creed 2. Regardless, it was very exciting to audiences. I believe this is still the best selling Assassin's Creed game to date.
Assassin's Creed 4 is mostly predicated on Assassin's Creed 3's formula, but it offered enough exciting new things (new setting, all the water and pirate stuff) that it kept like 85-90%+ of the previous game's audience and was very well received.
Where Ubisoft really messed up was in Assassin's Creed: Unity. The game's offering was basically "We have improved graphics, but we took out a bunch of features, and our main new feature (co-op) is only usable on side missions." This was basically a straight regression of the franchise, and the new feature was implemented in a way that was not compelling for most co-op centric gamers, so the sales went way down.
Assassin's Creed: Syndicate, while doing a good job of making sure the core game felt more fun, was basically an unambitious game built on top of Assassin's Creed: Unity's base. They even thought it was a good idea to cut Unity's main new selling point instead of improving it. People didn't like Unity, so no one wanted a game that was a small iteration on top of that. This was, IIRC, even a worse seller than Revelations, or at least close to it.
These days, Ubisoft is back to rebooting the entire series again a la God of War, because that's what is needed to get people interested.
(You will notice a trend here that people are pretty much willing to put up with one straightforward-ish iteration on a successful formula, assuming it does a good job of reaching the formula's true potential, but want another significant leap/change-up by the third game.)
So, wheeling this back to Fire Emblem, they essentially put out something that fit with the unexciting sequels of the Western gaming world, and received a sales drop in kind. It's easy to forget these kinds of impacts in Media Create threads because most of the games we discuss are very niche products selling to 100-150K people, and at an audience that small, it's easier to keep 70%+ of them even with a game that doesn't change much. However, once we get to these better selling games that hit a more broad audience, these factors really start to come into play.
Or, put way more simply, I don't think the issue was the lack of supports/romances (though removing or lessening popular features definitely hurts and they should definitely have strong supports/romances in the next game), but rather the lack of new and exciting features and ambitions. Given Fates was already the "improve everything" version of the Awakening formula, people were very ready for something new, so this was a double whammy, and led to the sales drop we see.