Probably not a good idea to make a wide open blanket statement like "More power is safer or less is safer".
If a speaker is rated for 40-400W, is a 40W amp safer or is a 400W amp safer if someone cranked the volume to max all day long?
What if the amp was a 20W amp or 800W amp?
Even if the 20W amp clipped and the amp didn't go into protection mode and shut off, would this very low power be enough to cause thermal and/or mechanical damage to a speaker rated for 400W?
Would the clipped power from a 40W amp be enough to cause damage?
I think we can agree that if someone used a 800W amp and cranked the volume to max all day long, they can say goodbye to those 400W-speakers because it would cause both thermal and mechanical damages.
I think if they cranked the volume to max using a 400W amp into 8 ohms all day, those speakers would be damaged also.
So if someone asks, "Is it safer to use more power or less power?", I think the answer should be "none of the above" because you should use the amount of power that is somewhere in between the max and min rated power.
If the speaker has a rated power of 40-400W, I think it's probably a good idea to use a high quality amp that is 100-200W into 8 ohms, not 40W or 400W or more into 8 ohms.