Medical care seems to have a lot of weird country-specific traditions, e.g. in Hungary it's apparently common to fill small kids' healthy teeth if the groves are too deep so they're simpler to clean and they don't get cavities.
I had never heard of such a thing before moving here, and I genuinely can't tell if it's a brilliant innovation or an insane post-soviet tradition that needs to go away.
Having experienced both (frozen and not frozen), I can't tell what's better. The feeling when they're digging in the tooth without freezing isn't great but it's not painful either; the feeling when they put a needle in your gum to inject the product isn't great either but then you don't feel the procedure. I'd say it's different but equivalent in terms of discomfort.
I've never heard this called "freezing". I assume you're being injected with lidocaine, the dentist's non-psychoactive best friend. https://en.wikipedia.org/wiki/Lidocaine
This family of molecules is well known for causing numbness in motor and sensor nerves; https://www.youtube.com/watch?v=KEI4qSrkPAs
Filling in grooves needs to go away. It will change the bite/shift the jaw which theoretically can lead to other problems. Not to mention, the grooves are there to help provide a grinding surface for vegetable matter, etc. If you make your teeth perfectly flat, they won't be as effective. Making your teeth flatter is actually reducing/damaging the effectiveness of your teeth. If it was a good idea herbivores would have teeth as flat as a tabletop.
Where I live, as a kid my dentist filed the tips of my canines down a little. Why? Who knows, they weren't bothering me before. It was something that was decided upon without consulting me.