Oh, I wouldn't give teachers cash either. But I thought we were talking about daycare providers.
For a teacher, it comes across as a bribe, since they assign grades to my kid. I only give gift cards to them, for the reasons frugalparagon mentions, usually to Target or Amazon. Last year, I asked one of my son's teachers if there was anything they wanted for the room. There was a certain book that was extremely popular with the kids, so I bought a second copy. I might do that again this year.
To me a big difference is that public school teachers are salaried and I don't directly pay their salary. With a daycare, the check you write directly goes to pay their hourly wage. In that sense, any money I put in an envelope is more like a bonus. I've heard that with nannies you should give them a money equivalent to a day's wage for the holidays.
We can pretend that there's not a difference between a daycare provider and a teacher, or we can recognize the differences in training and remuneration. This is the same reason I wouldn't give cash to a director. It's not appropriate. Maybe my daycare was completely different, but most of the workers did not have college degrees. They were lovely women who cared for my children well. No doubt about that. It was a hard and underpaid job. If your daycare has people with degrees and is more preschool-like then maybe it will be different, but if your facility has people paid $9 an hour who might need that extra money at Christmas to pay their electric bill (as mentioned above), then cash seems most appropriate.
I wish we could dispense with the idea that handing someone cash implies that you think they are poor, though. Visa or MC gift cards have gotten easier to use over the years, but they were a royal pain in the ass to use in the near past. You had to know the exact balance, and sometimes, if you didn't use it right away, a couple dollars a month would be deducted by the bank as a "user fee". Plus the giver pays at least $5 more for the card itself. I'd rather pass that $5 on to the gift recipient than put it in the hands of the bank.