Leave amps on?

The impedance of the speaker can easily make a difference. In some cases can change the class of operation too (lower impedance pushes the amps more towards the B region; yet another reason to avoid low impedance speakers if possible).

With a lower impedance load more current can flow through the output devices at idle. Since they already have a quiescent current (idle current), depending on how hard the output circuit is biased ('hard' meaning more bias current; perhaps the designer wanted more than just one or two watts of operation in the Class A region) reducing the load impedance can easily raise the temperature. I think you will find that with the other amp on the same load that it runs warmer too, just not so much that you notice it.

The impedance of the speaker can easily make a difference. In some cases can change the class of operation too (lower impedance pushes the amps more towards the B region; yet another reason to avoid low impedance speakers if possible).

That makes a lot of sense.

Class D amps are a better solution than Class a/b then perhaps in case of harder load speakers. A good one seems to operate much more optimally and consistently even with lower impedance/efficiency speakers.

Class A to do the job especially if speakers are less efficienct could be very large expensive and power hungry so not a practical option for many.

I often think if not for teh success I have experienced with good Class D amps, I would likely be more in the tube amp/easy load speaker camp by now. I’m glad I decided to try that first. I found it hard to find a Class A/B amp to do the job and sound as good as a good tube amp setup (with right matching speakers), but not the case with good Class D amps and most any good quality speaker out there today although finding the right sounding match there for each individual is still teh key to highest level of satisfaction.

Some of amps OK to be on, some of amps not OK. 
For me it's not OK to leave tube amp on if not used and so is for solid state class A amp as well. It will decrease their operational time by very very far.

It's OK to keep clas A/B amps on again as long as they don't dissipate excessive heat that may affect other circuit components and so is reliability of unit.

It's totally OK to leave Class D amps on 24/7 to achieve the best performance and longevity.