I mean I have some hunches on what could happen but it probably will upset some people. 

Firstly, it may just become a fact that games running off the main flash storage of the Switch 2 just run and load a lot faster and if you're stuck with SD Card or possibly even the cartridge version, you have longer loading times. And that might get ugly because if Switch games are struggling to feed the Switch 1's 4GB RAM (transferring data over quickly), well then obviously the situation is going to be worse with 8GB-16GB main RAM on Switch 2. 

If this pushes more people to buy digital ... well really Nintendo I don't think is going to be too heartbroken about that. They make $10-$20 more per game sold digitally than at retail where they have to give a retailer their cut, account for shipping fees, cartridge fee, packaging, etc. So if lower loading times are an incentive to push people into buying more digital and also potentially buying a more expensive Switch 2 model with more flash storage ... well technically it's hard to argue it's not a bottom line win for Nintendo, they're making more money. 

There are formats like UFS external cards and CFE which BofferBrauer pointed out above ... but these formats have either never taken and thus are harder to get or are mainly used by higher end camera/videographers/filmmakers and the cards are expensive. 

So the other solution is Nintendo could make proprietary higher speed memory cards, probably based around the UFS format, sold under their own brand. Of course this is controversial because Sony did proprietary cards with Vita, but in this instance Nintendo would have a valid performance reason, SD Cards just are extremely slow so they can argue they are just offering a superior alternative. But these cards would likely still be pricier than SD Cards. 

This works well for Nintendo though, because if you have to pay $70-$80 for a Nintendo brand high speed "memory card/drive", they obviously keep the profit, not SanDisk or whoever and if they're selling say 70-150+ million of those, well thats going to be a nice revenue stream for sure. 

All the cards on the video were UHS-I or lower that tops at 180 MB/s and the fastest one outperformed the switch gamecard  by 0.16 second but lost to the internal storage by 2.07 seconds loading Zelda. A UHS-II SD card tops at 312 MB/s. A  UHS-III SD card tops at 624 MB/s. 

I'm aware of UHS-II ... UHS-II cards just aren't that common, especially in the Micro SD format, they are generally full sized SD Cards and the Switch doesn't support those. 

But past that, 312MB/sec is still slow as shit. If Nintendo uses any moderately good more modern flash storage, it's going to be way faster than that. UHS-II cards also cost more and are harder to find.

If Nintendo is to offer a higher speed memory card, I think it's very possible they will just make their own based off an existing format (like UFS external cards) but make it proprietary and keep all that profit themselves and ensure the best compatibility and performance. But that idea is probably going to upset some people.