Why isn't Hagrid removed from Hogwarts sooner in Harry's would-be 7th year?

I can think of a few possible reasons.

1. Voldemort's regime was predicated on projecting a sense of normalcy despite his secretly controlling things behind the scenes. Hagrid's treatment is not that different than the treatment received by the Weasleys, who were allowed to continue to live normal lives while under constant surveillance. It's only once Ron was outed as traveling with Harry that they were forced to flee, despite their obvious sympathies from the start. McGonnagal, another former member of the Order of the Phoenix, is also allowed to continue to teach.

2. This was likely Snape's doing. Elsewhere in Relíquias da Morte it's mentioned that Snape has placed Hagrid in charge of "punishing" students by making them work in the Forbidden Forest. While certainly frightening, in reality it was far safer and less traumatic than being tortured by the Carrows. Snape faced the difficult task of publicly appearing to support Voldemort's regime while protecting the students and staff, so presumably he came up with a reason to protect Hagrid until the situation became untenable.

3. The Ministry previously attempted to arrest Hagrid in Ordem da Fenix. It ended with the Aurors getting their butts kicked and Hagrid running into the forest. His giant blood grants him a degree of immunity to curses and spells that makes him an incredibly dangerous opponent. Why not let sleeping dragons lie?

4. Conversely, a frequent theme of the books is the Death Eaters' arrogance and failure to understand the strength of those who are "beneath" them. In their eyes, Hagrid is an uneducated, feral halfbreed without a wand. They don't even kill Hagrid during the Battle of Hogwarts, only tying him up to mock him.