For living_street, the former discussion https://forum.openstreetmap.org/viewtopic.php?id=19316 seems like we should not used it in Thailand. By the way, stating it in the wiki is maybe too explicit, because it could be an appropriate case somewhere in Thailand, though it could be quite rare.
For service=alley, the former discussion https://forum.openstreetmap.org/viewtopic.php?id=62073 appears that we are unable to reach an agreement. I strongly oppose using this for the main access to the residence. The use, rather than the width of the road, should be used to define the highway=* tag. But if the road is too narrow for a motor car to pass, changing it to highway=path is acceptable because the use is different.
I doubt there are many actual living_streets as defined in the Wiki in Thailand. However, there are mappers in Thailand who use the tag despite the cautions in the Wiki. I much prefer highway=residential with subtags to further characterize the way in question; width, lanes, surface, max_speed. etc., if it’s located inside a gated community. Also, instead of access=private which would cause many routers to refuse to use those ways, I’ve begun to use ownership=private to tag driveways leaving the access tag out entirely. Perhaps that scenario could also be used for the residential streets within gated_communities. Many residential areas that are commonly called mubans in Thailand, I outline if possible and tag with place=neighborhood, name=*, and gated_community=yes.
Using service=ally is fine if it fits the description in the Wiki, which I agree with in general. Again, however, you’ll find some mappers in Thailand who use this tag a lot. See the thread referenced above by nitinatsangsit to get a picture of the long-running controversy.
To add to your list of places having actual service=alley ways, Anchorage, Alaska has them as well. Used for access to garages, utilities, etc. Same with Eugene, Oregon, two places I’m fairly familiar with. These alleys fit the Wiki definition perfectly.
While I don’t deny living_street could be useful in special cases (I know at least a couple of dead-end streets it could apply based on local knowledge),
using it commonly for standard, through-access, roads in gated communities goes against any of these definitions.
Would you let your kids play unattended in the streets of your Mu Ban?
Would you prevent a navigation router from reaching your house in your Mu Ban?
Is there known legislation/signage granting pedestrians priority over cars in your Mu Ban?