Try stuffing a DVD drive into a Switch. It's pretty easy to see why the optical discs wouldn't work in that application.
I would guess that the decision to use "cartridges" was a very practical one dictated by a variety of things, ESPECIALLY the tiny size and portable nature of the Switch handheld unit.
Besides, the durability and costs for hardware that uses solid-state cartridges, compared to an optical drive for reading disc-based media, was likely a very important factor as well. The optical drive would be more expensive, likely less durable, would likely use more battery power, would take up too much room in the handheld (room that could otherwise be used for something like a larger battery), would add hardware costs to the device for something like a door to access the drive, etc.
I've always thought the UMD drive in the PSP was super cool in a tech-gadget sort of way (literally like having a miniaturized Playstation, complete with discs!). However, the limitations of the little discs and the mechanical complexity of the drive were some drawbacks to the PSP system. Nintendo knows the Switch will likely be handled/abused by less-than-careful kids, so a delicate door for inserting disc media probably isn't the best approach for avoiding warranty repairs of broken products.
Finally, the storage capacity for things like SD cards is increasing and getting cheaper every day per gigabyte of storage. So, those little game cartridges for the Switch will likely just get cheaper and cheaper for Nintendo, and allow them to put larger and larger games onto them.
Edited by Retro-Z, Sun Mar 5, 2017 1:59 PM.