Doesn't any hydrophobic coating, by definition, repel water?
Yes, that is the idea.
But I think the concept of 'repelling water' is slightly misleading. Raindrops will still land on the lens.
LotoTec and AFAIK all the others create a situation where the base of the droplet that is touching the glass is too small in surface area to support the weight of the drop so that the drop runs off.
In my extensive experience of standing for hours in the rain in the Western Isles of Scotland with both my spectacles and binoculars equipped with LotuTec I can say that this system works well for medium and large rain drops. With these size of drops their weight is such that with the small area of base that LotuTec promotes the drops run off due to gravity. If the drops are smaller than medium then they don't tend to run off, but a vigorous shake will get rid of most of them.
Fogging produces a thin film of fine droplets which can be so tiny that they don't have enough weight to run off or be shaken off. I find that fogging doesn't happen very often, probably because we don't go out in cold enough temperatures. But it has happened in Novembers and has been caused by me pushing the bins too close to my face or lowering the bins to look with my naked eyes and accidentally breathing on an eyepiece. In these circumstances I wouldn't say the coating helps much, although to be sure the coating does make wiping and drying with a microfibre cloth easier and more effective than having no coating.
Fine mist-like rain acts more or less like fogging. It can cover the lenses but won't run off due to the small droplet size.
My wife has the same experience with her Leicas and I have the same experience with the Swaro EL SVs that I have been testing. They all work well with drops of water above a certain size.
I think these coatings are a great help and wouldn't go back to being without them.
Lee