I have been playing guitars for well over 40 years, and have owned dozens and dozens of them. I have changed the strings on (and done proper set-up for neck flatness, string action, and intonation) probably a hundred in all my years.
Though I can see that there might be some benefit from changing the strings out one at a time, I can also confess that I have never had a single problem result from taking them all off, and then carefully restringing, after taking the time to polish the frets.
As MickeyF stated, if your guitar becomes damaged from removing all the strings at once, it's probably not all that well made, or you made the mistake of cutting them off without first un-winding them to a slack state in the first place.
Bottom line, you can remove all the strings, and not fear that the sound of the guitar will change or degrade.