Here's a question: Do you think it's rude for the person to ask this question at the beginning, and to abort the game if you don't want to "play it quickly"?
Remember that their perspective is that they want to basically play it pretty quickly, but maybe there'll be some days that they can't get here, or they have a weekend where they won't login, or whatever. There's no real way to have such a time control, while still preserving the positives of turn-based chess. (I can login whenver I want, I don't get disconnected, etc.)
Thank you all for your comments on this! They have definitely given me some perspectives of thought that I had not considered. I was really surprised that this request is made in live chess also.
I have decided to just play at my pace, with my OTB goals in mind, despite my opponents request. If my opponent continues with the requests, or any other commentary on the subject, I will either disable chat, or just ignore his/her commentary.
Thanks again!