This ignores how terribly Monstrous Companion cripples your level, as well as the fact that most of those creatures are not options for Leadership because (as far as I can find) they do not have published effective levels.

If you allowed them it would be homebrew, and if the homebrew was based on existing data then they'd be as crippled as everything else. So all but maybe 2 or so of your listed creatures are straight out, even for that. The two I found on the Leadership list you linked that you mentioned, the Axioimite and the Shae, show how terrible they are as choice even for Leadership (let alone Monstrous Companion).

The Shae is a CR 4 creature with 7 HD that counts as a level 7 companion, which means Leadership can get it at level 9. However if it was an option for Monstrous Companion you wouldn't be allowed to have it until level 12, which goes from "bad" to "pathetic" unless you had something outlandish to pull with share spells via infinite level 1-2 shadow evocation.

The other one on the list I noticed, the Axiomite, you couldn't even take. It is effective level 14 (so with Leadership, get it at 16) for is already sad for CR 8 even with their abilities. However as a theoretical Monstrous Companion choice it wouldn't even be an option, since the chart tops out at effective level 12 at level 20 and has no available adjustments.

Some stat bonuses hardly matter to this. Leadership generally, and Monstrous Companion especially, punish you for taking anything with a high effective level... and they throw out some pretty extreme effect levels.