They have heard the demand for cloud saves, and I hope that they will come as part of the Nintendo Switch Online service.
I know that the argument is that they should have been there from launch, but I think many forget that, on PlayStation 4 at least, you need to be a PlayStation Plus subscriber to be able to use cloud saves.
There's a cost there that Nintendo (and other companies) clearly are nervous about and have to offset somehow as a business. I won't argue against Nintendo needing to work harder to compete in their online services, but it's understandable that after Wii U they probably weren't sure how popular Nintendo Switch would be. They focused on games to sway people early on rather than functionality and services, which is why, as part of broadening the console's popularity in the second year, they're starting to address that later than most would have expected.
We'll know soon in any case, seeing as the Nintendo Switch Online news was promised in early May. That doesn't help with your current situation (which sucks), but hopefully, we'll see them rectify it soon enough.