This is a really idealistic complaint that I think misses the mark and comes across as more silly than anything.
The reason why you haven't seen even more pushing of third parties by Nintendo isn't a failing of Nintendo; it's a failing of third parties.
When companies like Marvelous, Capcom, and Square stepped up to the plate, the result was Nintendo advertising them constantly. In fact Nintendo literally opened up their E3 2018 on a niche new mech IP that would have only sold at best hundreds of thousands of copies even with the best game quality possible. That's good advertising.
When Dragon Quest XI, a series which only would have moved a significant number of Switch units in Japan, was ported to the Switch ... Nintendo took the route of advertising it in every direct for a year, adding the character to Smash, and treating the release like it was one of Nintendo's own babies. Practically adopting a game as your own, because the publisher isn't that interested in pushing it in the West despite it being one of the biggest. That's good advertising.
Nintendo advertised things like No More Heroes and Bayonetta outside of just their own audiences, too, which is a very smart move as I feel these niche titles can appeal to gamers typically outside of Nintendo's ecosystem, and with the Switch being such an appealing console that just draws more people in rather than locking larger audiences out (like the Wii U did). That's good advertising.
I know it's a little different for titles like Astral Chain where Nintendo own the IP but, it's also worth mentioning that in that regard I feel Nintendo does a better job of advertising the niche titles they help to fund than someone like Sony. Astral Chain was given the same treatment as any Nintendo-made game would be, whereas something like Gravity Rush 2 was hardly advertised despite actually being created by a Sony studio.
Skyrim's port got a lot of marketing from Nintendo. So much in fact, that if you'll remember Nintendo was marketing the game for Switch before Bethesda even wanted to admit the port was real, despite the fact that Nintendo would probably get legal repercussions from pretending like a game which is not actually on their platform would be on their platform. THAT'S how much Nintnendo marketed Skyrim on Switch. It was paired up with Zelda in TV adverts, too, if I recall correctly. That's good marketing.
Mortal Kombat, DOOM, and Wolfenstein 2 were marketed similarly. I guess you could say DOOM and Mortal Kombat are the ones where aside from one trailer and maybe a sizzle reel Nintendo didn't market them a lot, but that's still marketing them and alongside that Mortal Kombat and Doom Eternal got a lot of Switch-related ads on Reddit from their publishers.
If it seems like the Switch doesn't market third parties a lot, it's just because there's not a plethora of them to market. In reality Octopath Traveler, Bravely Default II, Monster Hunter Rise, DOOM 2016, Wolfenstein 2, Daemon X Machina and Wolfenstein 2 all got extensive marketing. If they just don't seem that popular that might just be because some of those multi-platform games released later so their marketing push from the publishers themselves was smaller. But that's not a Nintendo problem, that's an issue of a platform holder holding up their end of the bargain and the publisher doing so limitedly.