Currently, Nintendo is one of the few developers in the industry who doesn't extensively use third party engine software. They've warmed up to its use in recent years though. Yoshi's Crafted World was built on Unreal Engine, and the launch title Snipperclips was made in Unity. But most of their games are still built on custom engines. That's not a bad thing necessarily, but with the Switch being so PC-like thanks to Tegra, it makes me wonder if Nintendo should leverage that more. Should they do more games in Unreal Engine 4 and Unity, especially with so many other Japanese developers using those engines?

Yes? No? Maybe so?

The question is too general and there are ultimately a lot of factors that we can't take into account as we aren't the developers ourselves. It's not like any one Nintendo game is known for having a bad engine, so it's a strange question. Yoshi's Crafted World isn't even Nintendo, that's Good Feel, a third party developer that makes games for Nintendo. Snipper Clips was also made by a British developer, with Nintendo helping co-develop parts of the UI, menus and art. But most of the programming was done by the indie devs themselves.

I get the feeling that third party collaborations use third party engines when it makes sense, which is quite often. 

It's either that, or 30FPS gameplay. Something has to give with UE sometimes.

Well that or they could have not used as many of the UE4 post processing and lighting features.  Yoshi is a rather advanced game in those areas for the Switch.

As for the larger question, most of Nintendo's internal studios seem to be doing quite well with their own tech.  Mario Odyssey and BotW bring in a lot of current gen rendering and post processing techniques with greater efficiency overall than a standard third party engine would without modification.  The Mario Kart team has done really strong work in the past with 8 and also on Switch with Arms, I would trust them to advance things on their own.  Monolith Soft had some bumps with the Xenoblade 2 engine but smoothed a lot of that over already with the Torna iteration.  I doubt they could get much better results from UE4 and there are some proprietary tricks on display, most obviously the volumetric cloud sim.  The Animal Crossing team maybe could, but I don't know how big of an overall benefit they would get.  Animal Crossing has a distinct look that I don't think requires a lot of the fancy features of UE4 and New Horizons seems to be doing quite alright anyway.  Splatoon is another matter, but again I feel they get most of what they need from their current engine and rebuilding their proprietary mechanics in UE4 just wouldn't be worth it.

The two teams I could see benefitting would be the Fire Emblem team and Game Freak (who isn't internal but still).  Neither has extensive experience in console development of high end, 3D games.  Much less HD development.  Now Sword and Shield and Three Houses don't look terrible, they're fine, but they are lagging noticeably behind the other big hitters.  Now Pokemon I am positive is feasible in UE4.  Fire Emblem should be, but their new emphasis on rendering lots of battalions could throw a wrench in that.  But still worth investigating.

So tl;dr, for the most part no, but there are a couple of exceptions.

Why would Nintendo use Unity? And i am pretty sure Unreal Engine 4 was the reason for Yoshi's delay

I don't think Nintendo wants to pay royalties to Epic any more than they have to. Their in house engines seem to be built efficiently enough to where games are coming out at a rapid pace so I don't think they need to use these engines. It might save time to learn and use the engines but again Nintendo likes to keep as much profit as they can.

Nintendo prolly doesn't want to pay royalties for that.

Also, I think they really value uniqueness in their games. I doubt they would want their games to look generic, or like the majority of big games out there. And besides, they're doing well on their own right now.

Their in house engines are clearly built for their hardware so it's likely that these engines are built alongside the hardware as it's being developed this not only allows them to do what they want for most part but also means they don't need to pay any royalties. I can only see them using third party engines for games where the is a straight forward template where not much tinkering is required to execute the ideas they have but for games like Zelda and Mario where the are a number of ideas and concepts coming together I doubt they'd used them.

It's possible we might be seeing Unreal more in projects worked on by side teams, again like Good Feel, that are tied to but not really Nintendo. I'm curious if there are any Good Feel esc teams we haven't seen yet.

(Pokemon and Unreal is certainly doable, but again we have no idea what is going on at Game Freak these days so who knows....)

No. Having your own engine that does exactly what you want it to, instead of a bloated engine that does a billion things poorly, speeds development. Nintendo doesn't want to pay anybody for anything. They like having their own console, publishing their own games, and using their own engine. Everything is under their control. Anybody else notice how Nintendo has always been a control freak? The fact that they let somebody make Cadence of Hyrule is bonkers. That, and it was no surprise that Mario X Rabbids turned out great. Nintendo wouldn't have had it any other way. I think they learned a lot from those CDi Zelda games back in the day.