The two products have some commonality of use but a different focus.
Both have their place.
Soap is used (as I know you know) for cleaning - it removes contaminants that are hard or essentially impossible to remove by rubbing or scraping or by use of water alone. It essentially must have water to work and it needs water to rinse it away after it has done its job. It's use as a sanitiser is important but a secondary result of its main role. ie by removing material from your hands (or clothes or elsewhere) it also removes contaminants that may cause disease. Soap by itself does not kill germs very well - instead it removes them. If the water source used with soap is biologically contaminated, the final rinsing off of the soap may leave your hands looking clean but actually quite 'germ' covered. If you washed your hands with soap in a small stream where there was a dead animal carcase slightly up stream, or where the water was faecally contaminated, there is a good chance that they would look misleadingly safe and clean. You could carry the water you used for washing, or for final rinsing, but the former would be undesirable from a weight aspect, and carrying rinsing water introduces unusual cleaning patterns (wash in stream, rinse from bottle) and also incurs a weight and volume penalty.
Hand sanitisers deal with germs by killing them "en situ". They do not primarily remove biological contaminants but instead render them inactive. Depending on the sanitiser used they may be a good solvent as well, so may be useful to remove a degree of soiling. However, the volumes available and/or used are usually small and sanitisers such as ethyl alcohol tend to evaporate too fast to be used as an effective gross surface cleaner when used in small volumes. Because they do not need to utilise a local water source they are immune to the effects of local contamination. But if eg you had blood on your hands, or faeces, or had vomited, the sheer physical overload of contamination could render the sanitiser ineffective unless you used very substantial quantities.
So - the idea is to have both available, with soap as your primary cleaner, backed up by sanitiser where there was a clear need, or where you were uncertain. In most cases sanitiser is unnecessary. The hardy pioneers never had it (or, rather, they preferred to drink it) and even now, soap is often enough more a luxury item than a necessity for many hikers :-). However, there are occasions when sanitisers will keep you healthy, or alive, when soap won't. It's a good idea not to have to rely on hindsight to determine when these occasions may be :-).
I have travelled quite a lot in Asia in recent years - cities and travelling rather than hiking. I try to ensure that I have a small bottle of sanitiser with me at all times - no exceptions if possible. And, I seldom use it. After you have used a few 'squatty' toilets in typical conditions, and then gone to eat a meal, with or without the availability of a water supply for washing, having sanitiser to hand (literally) becomes very attractive.
Some dislike sanitisers because of the perceived (or actual) effects on skin, their lack of naturalness etc. Each must decide for themselves the merits of such concerns.
More soon ...