Most people do expect timely replies to emails. If you act like taking days to respond to an email is normal, people will get very upset with you.
In most contexts days is perfectly normal, and expecting a faster reply, especially without explaining why it's urgent, is considered impolite. This includes all the cases where the job of the recipient is not literally "reply to e-mails ASAP".
I won't. Days is ok. For non-urgent emails, I would only be slightly annoyed if it's been more than a week, and I'll then send a reminder.
It's ok. I know you're busy, take your time and respond at your convenience.