A few thoughts:
1. There has to be a clear statement about using animal companions/familiars as sidekicks. I'm fine if it's allowed, as long as there is an "only one sidekick per PC" rule (and of course DM's permission). Not to allow familiars makes them objectively worse than the sidekick, which shouldn't be.
2. I want to think about the implications of this of a mount. A Mastiff or Horse as a sidekick is a substantial change for a cavalier or Paladin.
3. There should be a statement to the effect of, "The first time you level up with a sidekick, the sidekick advances to your level" (or your level minus x, or whatever). Gaining a level 1 sidekick at level 10 is less effective (mechanically, and in terms of the narrative survivability) than gaining one at level 3. But you should be able to get a pet and be equally effective at upper levels as getting one early in your career.
4. What are the costs of having a sidekick? There should be something. Is it another character with whom to split experience points (assuming points are used; if they aren't there are other issues)? I could see having a sidekick counting as .5 of another character -- but it does mean that PCs without a sidekick could be "dragged down" by a party with pets. It's not immediately clear what an acceptable solution would be.
5. My favorite part of the article is that the Expert or Spellcaster class needs to have a language. All of a sudden, the fact that Blink Dogs and Giant Eagles have a language of their own has meaning! I love this (emergent complexity, as a latent detail gains purpose), and I look forward to my friendly Blink Dog spellcaster barking my PC back to health.