This seems like an interesting solution, even if it's absurdist at first thought. What if we just shift the steel bar in Greenwich 20 metres east or west instead of adding a leap second?

Then everything would theoretically be correct. The logical next thing to do would be to move all the time zones as well. But time zones already don't coincide with the lines of longitude in practice; they tend to follow country or internal boundaries somewhat close to the lines of longitude (but sometimes multiple hours away!). After a few thousand leap seconds, maybe one or two countries would feel it was helpful to readjust a time zone boundary to better align with solar time, but in practice this would never be the overriding reason for that decision.

You say people's GPS systems would all suddenly be wrong because they depend on locations in latitude and longitude? I don't think this is a problem either: in practice longitude and latitude are given not relative to the steel bar in Greenwich, but to per-continent geodetic datum points. This already prevents continental drift from affecting your coordinates, though a big earthquake can still mess things up.