I think the knowledge that the set is countable and can thus be counted is, as you say, quite obvious. However, actually counting it or generating the complete

I think the knowledge that the set is countable and can thus be counted is, as you say, quite obvious. However, actually counting it or generating the complete set is terrifically hard in practice. There are many more illegal positions than legal ones (I suspect, would be curious to know if this is actually the case). Moreover each legal position may be the result of thousands of games played legally or thousands of games played illegally. Computers historically haven't been able to enumerate this set, or judge from a position if it is conclusively legal or illegal since the complexity of that question is immense. We're on the cusp of being able to do that and I think that's what makes this project more than a trivial exercise in counting countable things.