Well, from what you posted, it seems like way more than 15 min. per night for a 1st grader to do. I have no problem with that as long as it's not busy work and benefits the child. Now in high school, yeah 30 min. is not a lot, but when you mulitply that times 6 classes, it's a lot. Even if only 3 teachers assign 30 min. per night of work, that's another 1 1/2 hours of homework on top of what they've already put in. I have a high schooler who is near the top of her class. Some nights she has hours of homework -- beyond ridiculous stuff like 7 grammar sheets (pure busy work to me because honestly, we don't become good writers by doing grammar worksheets), 3 chapters of reading plus notes, some type of long-term project that needs some attention each night, 20 minutes of math, and about 30 min. of chemistry. To me that is way too much and it doesn't help her become any smarter when it's all busy work.
DH and I are both teachers and I'm privvy to the homework research on both sides.
Now I never did address the assessing concern you had in your original post. Good teachers let assessments guide their instruction. If a teacher is testing just to test, then that's not good. But if a teacher assesses and then adjusts his/her teaching to meet the student where he/she is at, then I'm all for it. Also, when a teacher assesses, they are not always just looking at right and wrong answers. They are looking for patterns which aren't seen if a teacher is just trying to store all of that info up in her brain when working on informal assessments. Maybe the teacher is doing too much, but then you should not worry about it. It's only 1st grade! You'll have much bigger fish to fry later on.