It is complicated by life not always being just.
I was thinking along the same lines after kibbing the following:
A team game, imps. At the other table a forcing NT auction had them playing in 3C, but at this table they landed in 3NT.
The opening lead was the heart 5 to the A, the 9 was returned won by the Q. It seemed pretty clear to us in the gallery that a spades should be played next, but a third heart was led and declarer scored up his game.
Honestly, even if I had the option of 1S-3C to show a natural invit, I am not so sure that I would have used it here. That N hand is pretty good. I gave the N hand to a f2f partner today. We do not play 2/1 gf, so bidding 2C and then 3C is passable. But even if that is so, I am not so sure that, as S, I would pass 1S-2C-2D-3C. S could have less.
My thinking is that if 1S-3C is natural and invit, an approach that can be useful when it arises, it should deny having two cards in the spade suit. So this hand and your example hands, qualify.
I think somewhere Mike Lawrence recommended just bidding the GF 2C and hoping for the best. This worked on the hand I was watching.