Yeah, the switch mini strikes me as a really daft idea (although you never know with Nintendo, haha). A smaller screen will make some games harder to play (I already struggle in handheld to read the text in some games). No multiplayer out of the box. Not compatible with the current dock. Even worse battery life. And I'm not sure there really is that much demand for a smaller switch anyway. The 3DSXL massively outsold the standard size from its release for instance and consumers seem perfectly happy with big phones (I'm typing this on a 6.5" phone). This notion of the importance of 'pocketability' is just silly and I don't think the vast majority of people care.
I really don't see how it would be worth Nintendo the R&D expense of squeezing the switches internals into something even smaller when the market for such a device probably isn't all that large. Are there really that many people who won't ever buy a switch until it's much smaller? It would surely make more sense for Nintendo to keep the current form factor and joy-cons but cut the price and improve the battery as technology allows, etc. But yeah, you never know with Nintendo...