No, it's not possible.
There are rewriteable Switch Cartridges and a HAC-Writer (Cartridge Writer for Nintendo Switch) for Developers but the Cartridges does not work with Retail Games or Retail Devices.
They only work on the HAC Dev Unit.
That would only work if someone could mod the dev kit to run retail games so it needs a hack... Games have their protection and the dev kit doesnt also run protected retail games...
Its not as easy as just getting some game retail dump and put it into the devkit to run, they first need to do a lot of work, so either way we are stuck for now
However you can make your own stuff to run on a devkit and for a game developer I think this is such a wonderful device since its probably the most portable high performance gaming device on the world to run your games.
From what I can tell, the EDEV model (similar to retail; has minimal debugging functionality, sort of like RVT-R and CAT-R units from previous generations) is around $750, or $1000 for the 64 GB model.
SDEV, which has a bunch of extra ports and can't be run off of battery, costs significantly more.