That's exactly what happens via the unequal distribution of federal income to the provinces.

We can argue that it's a good thing the program works the way it does and I'd argue, for the most part, that's true [0]. But all the programs you listed and the eq. program are net transfers from rich (and less politically powerful [1]) to poorer provinces.

It's akin to when coastal Americans bemoan that fly over Americans get net transfer of wealth from them.

[0]having lived in many US states, I kinda like knowing that NL, or NB is taken care of when they're in the dumps

[1] Being a 905er myself, let's be honest here! Quebec, between separatism and as a battleground province, can throw a hissy fit and get whatever they want (and good for them! Hate the game, not the player.)