There is one important fact to consider...
Leather is pretty amazing stuff. I have some odd pieces of veg-tanned cowhide on my shelves that are 10-15 years old.
They have NEVER been treated with any sort of leather conditioner, and are still in the same fine shape they were in when they came from the tannery.
The reason for this is that unless leather gets used (and abused,) it retains its natural oils. And by 'abused' I mean getting wet and drying too fast, getting muddy and not cleaned, or getting sweat-soaked (salt) and not washed off. (Yes...'washed' with soap and water! It's good for leather!) Leather saddles made from vegetable tanned cowhide, if kept clean, only need to be rubbed down with leather conditioner a couple of times a year even if they are used daily, get rained on often, sun-burnt, and butt-pounded all day! Just a little bit of leather conditioner will keep a working saddle healthy for a lifetime. In the case of leather conditioners, 'more' is not necessarily 'better.' The leather will only absorb as much as it really needs and no more.
Then think how much 'abuse' a strop might get... or, in reality, doesn't get.
When I see a vendor selling 'strop conditioner' with the advertising copy; 'to keep your strop in good condition use daily,' I have to wonder at the integrity of the vendor.
Stitchawl