This isn't really the case with the Switch though, as per Nintendo's own numbers for several years now 3rd party software sales has been 50% or more of Switch's total software sold (and that doesn't include digital indie games either), so the majority of Switch owners are buying 3rd party software to some degree it would seem. 

600+ million in 3rd party software sold is pretty massive, yes maybe it's not as big as the PS4-PS5, but 600-700 million 3rd party games sold is probably in line with a system like the XBox 360 (Microsoft's peak in the industry).  

Who looks at the XBox 360 and thinks "well that wasn't a heavily 3rd party driven console". If Nintendo is getting in that range of 3rd party sales, that's significantly higher than what they were doing in the past and likely bodes well for higher support in the future as it's hard for a developer to look off a market that large. 

If Nintendo can be in that 450 million-700 million 3rd party games sold range, they would be in pretty good to great shape, this is probably a lot more than previous Nintendo systems, even more than the NES, SNES, and Game Boy (yeah obviously the overall market size was smaller back then) which are known for 3rd party support. 

Sure, but since the question was what it takes to increase the (already quite high) third party sales I still think that the significant subset of games sold is first party is relevant. Especially if one compare to the much smaller subset of first party games on other platforms. 

LOL.

Switch has sold over 1.3 billion units of software.  If 80% of that is first party that would mean Nintendo sold over 1 billion units by themselves.  Use some sense man!

I don't think it really needs to increase that much. 

If 3rd party game sales are about half of that 1.3 billion, that's 650 million and climbing ... I mean that's probably about the same number of 3rd party games the XBox sells, and it's unquestioned that the XBox gets basically every major 3rd party game except for the small handful of 3rd party games Sony money-hats away (and even those pubs like Square-Enix are pushing back on doing that because it's an idiotic strategy that isn't paying dividends). 

With Switch 2 I think the ratio of 3rd party games to 1st/2nd party will naturally increase too simply because Nintendo won't be able to make the same number of games most likely. 

As it has been mentioned, 3rd party sales on the Switch have not been bad at all ( I remember reading about the Witcher 3 port that was 4 years late selling 2 million or so). With that being said, I don't think ( at least at first) sales could reach the level found on Sony's systems even if the versions were the exact same and came at the exact same time simply because Nintendo's ecosystem is just not the same.