Potency of Rook or other piece pinned on King

Is it not, perhaps, illogical that a piece pinned on the King should,though unable to move, still be effective to give check on the opposing King?

Logic has nothing to do with it. Any piece can control squares; protect another piece; and deliver check/checkmate without the need to move. Why should special rules apply to a pinned piece ?

Not illogical at all.

Just pretend that the game really ends when the king is captured. If you move your king to a square covered by a pinned piece then that particluar piece would take your king before you had a chance to take advantage of it.

Even two years on I am not sure I understand the above answers to my query which was actually intended as a contribution to a forum on hypothetical changes to the rules.The point is that with the single exception I mention pieces[or pawns] move or can move in order to 'capture'.

Think about it like this: why can't a pinned piece move (if it's pinned to the king)? There is no rule about a pinned piece not moving, the specific rule is you can't move so that your king is captured (the king is never captured in chess).

So if you agree a piece pinned to a king can't move for that reason, then you should also agree that a king can't move into the attack of a pinned piece because then that king could be captured. If you like, you can think of it as which king would be captured first: the king that moved into attack first.

The idea that a pinned piece is rendered inactive, so to speak, is just a useful shortcut for most cases. The actual rule is you can't give up your king, and it applies to both players!