My general feeling is that when playing the "why isn't x on y since something similar to x sold well on y" game, often the perspective of the discussion becomes extremely narrow and ignores several factors in reality.
It is extremely easy to say "Hmmm, Fire Emblem sold 500k on the 3DS, clearly there is an audience for this sort of game if done well on the platform, we have an IP which used to be right up the alley here, let's do that." in an isolated and detached way. Does it make sure? Yes. Would such a project be profitable? Certainly. But does this actually apply to the business reality of the companies who could be making this statement at the time? Probably not.
Game development can take 2-3 years to complete, especially when there isn't a smooth and regularly tested development cycle for that project type. A developer who regularly makes the same type of the games every year or every other year would be in a better position than a developer who has to make something they have never made before or hasn't made in a long time.
To make a good game in a given genre, you also need people who know how to do that. I would say the reason why Strategy RPGs seem rare is because good SRPGs are hard to make. Even if we go back to the "golden age" in Japan, the ones we remember the best would be TO/FFT (Matsuno), TO:KoL/FFTA/FFTA2 (ex-Quest), Fire Emblem (IS), Tear Ring/Berwick (ex-IS), Arc the Lad/Front Mission (G-Craft), Langrisser/Growlanser (Masaya). These are the ones which sold the most off the top of my head, and they all basically originate from a few core developers - Quest, IS, G-Craft, and Masaya. There were a lot more junk in the genre in the past too, but most of them didn't really sell much. In today's climate, since everything already sells less, publishers who aren't going to put effort into making something great in this genre are more likely to just go the mobile route.
There are still a number of SRPGs made regularly which don't sell anything like FE though, so that's also a sign that it's not a pressing demand in the genre itself, but a demand for something like FE in particular done well. Disgaea, other Nippon Ichi games, tons of Idea Factory games, Sting games, even the Devil Survivor series from Atlus. They exist, they're just niche. So publishers are also going to look at that and consider that FE is an anomaly rather than a representation of the demand for the genre.
As for what happened to the people who used to make the biggest SRPGs I mentioned above, well, I think a bunch of them just moved on. Matsuno has left S-E and Level5, he's completely freelance now and doesn't seem to want to commit to a major project anytime soon. The ex-Quest guys who made FFTA have all been absorbed into the FFXIV team as Nirolak mentioned. The G-Craft team which joined Square Enix used to be headed up by Tsuchida, but after FFXIII he left the company and joined one of the big mobile cash-in companies. I have no idea what happened to the Tear Ring/Berwick guy, he seems to have just given up after Berwick Saga. The remains of Masaya staff who worked on Growlanser back in the day was absorbed into Atlus, they're the people making the Devil Survivor games. Hardly as popular as Langrisser was though, so I doubt Atlus is looking to push the series much more. I hope they do though.
So yeah, that's basically why I think big SRPG titles are kinda dead. It's a hard genre to really make well in a way that really appeals to a larger (>200-300k) audience, and the talent the industry had to make such titles have drastically contracted. It would be nice if new talent popped up able to do that, but I guess publishers aren't interested in taking that risk when there are lots of other things they can put resources towards instead.
