Is it impolite to not to respond to professors' replying email asap?
In the US, many professors really don’t like the idea that students tremble in fear at any interaction with them, and/or regard them as a class of semi-divine beings who need to be constantly flattered and paid homage to. Any idea that the student’s actions are motivated by ideas like

“hierarchy”

“I should not bother to send another email unless it includes a considerable amount of new information”

“I should almost always send the last email”

“professors can ignore me but I cannot ignore them”

“lower people are expected to show more respects and do more works to maintain the relationships”

“Is it impolite to not to respond to professors' replying email asap?”

etc


will be seen as upsetting and in many cases offensive to such professors.
The standard etiquette in the US is therefore to treat the professor with the same respect and professionalism that you yourself expect to be treated with (and that any professional person ought to expect to be treated with) by anyone in a professional working environment. That is, if the context of the email requires an urgent response, then you should answer with a corresponding urgency and immediacy; and if it doesn’t, then you should answer within a time frame that makes sense for that context. The fact that you are a student emailing a professor has no effect on whether the time interval to answer an email is polite or impolite.