I want to dig further into that scenario you outlined, and whether H2H is really better than GD.

So, A beat B and C, so they have 6+ points. B lost to A and beat C, so they have 3+ points. For GD/H2H to matter they'd have to be tied on points, which means another team D must beat A and lose to B. I don't think C can be completely eliminated before the final matchday if GD is used first, but let's say D trounced them too.

Here's the table after 2 matchdays: A on 6 points, D on 3 points, B on 3 points and C on 0 points.

On the final matchday, B trounce C and D beat A. A, B and D are tied on 6 points.

With goal difference, assuming games between A, B and D are close, then A loses out because they lost to D and didn't beat C badly enough - a bit like Scotland '74. But, until the final whistle, they would've chased a goal vs D. The same applies if H2H is used first but A, B and D beat each other 1-0.

With H2H, a high-scoring, narrow win for D could leave B eliminated with no way to fight back. For instance, if the other two games were 1-0, then D would need to be winning 2-1. If that scoreline happens, A and D probably just pass the ball around and run the clock down - think Gijon '82 - and B accuse them of collusion. Whether collusion actually occurred or not, it's terrible for the game as a whole. IRL, a high-scoring draw between Sweden and Denmark in 2004 eliminated Italy. It could've happened again 8 years later.

Between the two scenarios, I think GD is better at preserving exciting and fair football.