@Chris11487 It is indeed regrettable that Airbnb displays the lowest available nightly rate, excluding all fees (including their own), in search results-- until you enter your travel dates and guest count, whereupon it displays the total cost. And of course, you always see the total cost before you book.
As a host who charges a cleaning fee this is frustrating to me, as well. I have no interest in wasting the time of guests looking for lower-cost options.
My cleaning fee is a fixed cost. It goes directly to my cleaners for their labor and supplies. My nightly rates are set automatically by pricing software, according to local supply and demand. Sometimes that means they drop below the cleaning fee. You suggest "Cap the cleaning fee to not exceed rental rate." Well, what that really means for me is: set the nightly rate minimum to never drop below the cleaning fee. Would that actually be better for anyone?
It would be great if Airbnb's search results were more transparent, saying "FROM $$" and "Please enter dates and guest count for accurate pricing."