Maybe it's lost in translation, but I'm not sure how exactly it's creepy to offer to take care of someone who is sick when they've done the same to you.
Then again, dense protagonist disease is a thing.
@Majora Yeah, especially considering they like each other so much and get along, so there's plenty of trust between them. I'd guess Takeda only thought so because he's trying so hard to respect Takizawa as a boss and is all the time worried he's crossing some imaginary border to be too casual in her company. For a man to offer to visit a female superior's home when she's sick isn't something one would normally suggest just like that.
@Majora Yeah it's a bit lost in translation
Let's be in super creepy mode "I can not wait to see you falling sick, in order to going to your house, just the both of us, to "help you".