Make sure some cells are protected and that some are not, for example you can 
unprotect the columns A-B and D-E and let C be protected.
Protect the sheet, with or without a password.
Now select a range of cells where some cells are protected and some are not, 
for example A4:E9.
Hit Delete or Backspace.

Nothing will happen, because some of the cells in the range are protected and 
the sheets is too. Actually, not even an error message pops up…! It does 
however, when I try to delete one single protected cell.

But what do I want to happen when I follow the instructions above?

Well, in most cases I want to delete all the cells in the range that are not 
protected and let the rest of them remain as they were.

This is convenient if I enter numbers in a few ”input columns” and some other 
columns – protected – contains formulas that calculate things from the input 
columns. If I want to clear out all the input data and start over, it would be 
very convenient to just select a big range of cells and hit delete, and all the 
cells that are unprotected will be deleted. Then I don't have to spend time 
writing a Clear Sheet macro or to do a complicated (in some cases) multi 
selection in a sheet.

I can accept that a dialogue pops up asking me before deleting, though, or a 
setting somewhere to determine the wanted behaviour.

Hope this make sense to anyone else. I have been thinking of this for several 
years now so maybe it's time to report it, I thought…