To bit slightly pedantic on a few points of order. The TSA has no rules regarding the size of carry-on, only the airlines do. If it exceeds any given airline's allowed measurements, it is not a carry-on any longer, but a piece of luggage that should be checked, but potentially can be brought to the aircraft. Even if there were a TSA rule, it would have no bearing on a European airline operating in Europe.

That being said, I have very rarely seen sizers in use for SK, probably only in Heathrow. But I have seen judgement of size at the gates followed by weighing. And I have seen items checked for weight, and that usually means items go in the hold. Checking does seem to be more the exception than the rule.