As I said in a previous post;
"Strop dressings are made for use on bare leather strops... I've never used any sort of strop dressing on compound-covered bench strops (some of mine are 20-30 years old and still going strong,)"
You really see the benefits of a leather dressing on leathers that need to flex. As David says, cleaners will strip leather of its natural moisturizers, (as will heat and sunlight, salt, and rapid drying after getting wet,) and dry leather can crack when flexed. Saddles, bridles, harnesses, baseball gloves, motorcycle jackets and chaps, and of course, barber's HANGING strops... all leathers that flex and bend, or may get exposed to harsh environmental conditions in normal use. Re-vitalizing these sorts of leathers becomes imperative for their longevity.
Bench strops or paddle strops? Especially those already 'sealed' by a coating of wax? Nah.... These should be good for the next 50 years of daily use without ever seeing a leather conditioner. With an application every few years, they will become heirloom items.
I'm beginning to see in the Sharpening Hobby similarities to Divorce Proceedings...
In a divorce, a man and woman may be comfortable (not happy, but comfortable) splitting up, and able to work out an amicable agreement to divide property... then the lawyers get involved and what happens next is close to warfare, with the lawyers making a shitload of money 'advising' their respective clients of what is 'best' for them. In the Sharpening game, we hobbyists seem to be able to discuss our needs together comfortably... until the Vendors get involved 'advising' us of what is 'best' for us... and making a shitload of money selling us stuff we really don't need.
I'm not getting old and cynical, am I?
Stitchawl