@icekatze A lot of this issue comes from the fact that one: she's a woman(gotta remember the time zone of the story); and two: even if she is a favored maid, she is still nothing but a lowly maid. If people hear that she's been advising the emperor when they know nothing about her (especially her origins! Some people legit thought she might be a spy, and probably still do) then there'll be a huge amount of discontent. With that said, she has done a lot to help the empire thus far. My hope is that he will try to marry her, people will get upset, and then at that moment he will reveal the truth with proof about everything she has done for the sake of the empire and it's people as a way to prove why she is worthy to stand next to him on the throne.
Also, regarding her being a woman and Rachel being a woman, Rachel is a known noble daughter who is a candidate for the empress's seat so of course the empress should be knowledgeable and capable in order to assist the emperor. There is a huge difference in Marie's status as an unknown maid and Rachel's nobility status as empress candidate.
And lastly, he doesn't know what she wants iirc. I don't think she has explicitly expressed her desire to leave the empire(but I could be wrong), so Rachel intending to give her what she wants is literally just luck on her part. As for the emperor, those favors he's been trying to give her is his way of repaying her for everything she has done as well as his intent to keep her close, both because of her capabilities and, as is evident in this chapter, his not-so-obvious romantic attraction to her.
This series is not perfect, but there is reason for many of the "whys" and "hows." Notice how I said "many" not "most." There are still quite a lot of plot holes that need to be filled.
Edit: Btw, everything the emperor has done has been with good intent, while Rachel's intent has been more malicious. Not overtly so, but her intent to send Marie away was not as a favor, but as a way to get rid of her, even if Marie would gladly take it as a favor regardless. There's a reason why she is being regarded as a villain.