How much of republicanism can we get without making any essential reference to domination? Maybe quite a lot.
First, whatever job the government has, if carrying out this job requires substantial power that is liable to abuse, then part of your political ideal should be republican democracy (and you should be very leery of even putatively ideally benevolent dictators). In particular, you might want a high level of assurance, born in part through moral recognition, that the government or government officials will not behave like the criminals that they are supposed to protect us against (supposing that this, at least, is part of the job that governments have). Just say no to a charter city run by Elon Musk or whatever.