In my first year of teaching, all staff's home phone numbers were provided to all families. Another young teacher and I complained about that and had them removed for the next year, but all the existing staff had put up with phone calls to their homes for a few years prior to that. Why they hadn't complained about that is a mystery to me.
OP, I think you have a right to have your DD's info removed from any website you like. That's fine.
I get the impression, though, that you think that your DD's teacher is sitting around all day with all the time in the world to work out the personal communication preferences ofthe parent of every student in her class, and write personal notes to some, call others etc. Teachers just don't have that time and that memory. It really is a much bigger drama to write notes in homework diaries than to write an email often. I can type much faster than I can handwrite a note. I can edit when I reread it if I think I've been too harsh, or not given enough information.
You seem to feel that the school should be doing things on your schedule:
Our teachers call before school , altho they do not get in officially til 8 30 at DD's school, or when the kids are at their 'special' (gym, library art, music). Again, with the load of work my DD brings home, I realize the teachers have a lot to do, but the teachers expect the parents to come to the school for conferences and school events during their work day and they really push for parental involvement when things are scheduled 9-5 so it is a balance of trying to accommodate everyone's schedule. Last year my DD's teacher would send emails during the day about an issue with DD (not behavior but important) but as I was not allowed to check personal e mails at work, I didn't get these until evening, usually after DD went to bed. I finally said she had to call me if it was imperative because if not, I wouldn't know until I checked my emails after the kids went to bed. If not, write a note in her homework folder and I would see it right when I got home.
Other parents' schedules aren't the same as yours, so these might work fine for them. I, as teacher, can't remember the best schedule for 30 kids and their parents (many more for other teachers): which can read emails during the day, and which prefer a phone call after 6, but not during dinnertime, which is between 7 and 7.30, which are available for daytime events, but only every second week when they're on afternoon shift. Schools operate between 9 and 5 - when else would you like events to be scheduled?
And it's great that you read your child's homework diary as soon as you get home, but that's not going to be the case for many parents: they'll get an email when they're on the bus home in the afternoon, and won't see the homework diary until the next morning.