Online emulators are crapware. You don't know what other code they're running on your machine, you don't know if you're playing a legit copy or some random ass hack, and most importantly it's a quick route to randomly losing your save data. Also those sites are far more likely to get targeted by copyright enforcement.
Plus, if you use a decent emulator, you can often tale your save files on the go. Retroarch can be a bear to set up, but I can play on my big monitor at home and pick right up on my phone later while I'm waiting at the doctor's office or something.
I don't know if I would high-horse water bottle it. What you've said is true of any website or even downloading emulators and roms unless you've created the rom yourself with the original. Your statement makes it seem like that process is completely safe and making it a false sense of security. You can gain confidence in a source but that's never a guarantee.
The saving file is definitely a bonus and being able to secure an emulator on a non-networked device is even better. I just threw up the online emulator for that instant itch nostalgia hit if the person wanted it. Chrono Trigger is a very long game if you explore enough, wanting to play it and being to actually play the entire thing is sometimes completely different. I'm definitely grateful for the resources you posted up so they can follow through with that path if anyone wants to go all the way.