It sounds to me like you all are saying that =designated has a very specific meaning (which apparently I don’t actually understand 
) and only applies in certain countries with particular types of laws. Prior to this discussion, that was not my understanding of the meaning. My understanding is based on these descriptions taken from the wiki:
A way marked for a particular use
A preferred or designated route for the class of traffic specified
indicates that a route has been specially designated (typically by a government) for use by a particular mode (or modes) of transport
The value designated is not meant to imply that OpenStreetMap access=* permissions have been automatically “designated” only to that transport mode
The language on the wiki recommends the use of =designated in any situation where a sign indicates that a way is intended for a particular mode of transport. It says nothing about strict legal requirements.
It sounds like you all are saying this is an incomplete description and that =designated is a value that should only be used rarely. If this is in fact the case, it sounds like the wiki should be changed. However, I still don’t understand what the specific cases are where =designated should be used. All I’ve understood so far is that you all say it shouldn’t be used in the examples I’ve put forward!
My primary use case for =designated has been on trails in the backcountry that are managed primarily for one use type, but other uses are also allowed. For example a trail may be managed for horses & stock animals, with hiking also allowed but not the primary use. I would tag this as highway=path + horse=designated + foot=yes. It sounds like you are saying this is not correct, but if =designated is not to be used in a case like this, then what is it for? I’m sure someone will be quick to say that in this case, highway=bridleway + foot=yes should be used instead. However, that type of tagging only works for horse, pedestrian, and bicycle focused ways with bridleway, footway, and cycleway respectively. Other transport modes do not have highway=*way tags like highway=skiway, highway=snowmobileway, or highway=atvway. So highway=path + atv=designated + bicycle=yes is the only way I know of to tag a trail that is managed primarily for ATV use, but where mountain bikes are also allowed secondarily.
If the understanding I’ve developed so far is incorrect, I’d appreciate any further clarification on how the =designated value is intended to be used.