Is the Mechana Initiate worth buying (except at the end to get some easy points)? It's only 1 Rune or 1 Power, which seems weak compared to the other Initiates.
The key thing with the Initiate is the flexibility. While often weaker than other choices, sometimes that's all you have available. I've seen some games where only the Mechana Initate player was able to afford some of the power cards due to that flexibility. It's true that he will increase the size of the deck, so if you're going for a power-combo deck, then he's likely not a good choice. However, if your deck building is based more on value-per turn opportunities (score rushing), you can often win before combo decks get going. This initiate will be key that that kind of strategy.
Late-game, it's a reliable way to get one honor for one rune. If you're not going to be cycling through your deck again, the goal of buying cards is to maximize the value of what's in your deck.
I'm not sold on the Mechana Initiate as a good card. The flexibility IS nice, but you're choosing between making it a Militia or an Apprentice -- two cards you'd be well-advised to aggressively prune from your deck. It does very little to help you either purchase the big-ticket items or go big game hunting.
In the early game, I suspect the correct move is to ignore it and let somebody else clutter their deck with it.
I've managed to play many games on digital with all expansions to date which include up to Dawn Of Champions, and even several promos. There's already been some good answers concerning "in general", or for just that set (base game/CotG). I'll also add...
Copy effects so you can get both a rune AND a power (although yeah... it's still only 1 of each, and usually more rare where you'd need 1 of each).
Use as "cannon fodder". If you have an effect that forces you to banish or discard a card, may as well be that if it can't be a Militia nor Apprentice.
If it's an effect where you get to acquire a card of "up to x more honor than the card you banished", then you count from 1, whereas banishing a Militia or Apprentice is considered 0 honor. For example, you can Banish a Mech. Initiate with a Storm Of Souls card, and acquire a card that is up to 3 honor, not just 2 (2 more than the banished card in this case)!
With Realms Unraveled (exp #6), there are cards which give you a bonus if you've played 1 or more Mechana Hero(es). He's a cheap way to get to that!
With Dawn Of Champions (exp #7) there are cards that give you a bonus if you play any Mechana card (hero or construct).
Another thing with DoC is there is the "Champion" mechanic where each player starts off with a random faction (Enlightened, Void, Lifebound, or Mechana). If you're given mechana, all mechana cards you acquire will give you one Reputation. Normally, you add Reputation by paying 2 runes, and that method is limited to once per turn. If there are 2 Mechana Initiates in the Center Row, 2 runes to buy them gets you 2 Reputation!
Because of DoC's crazy Rally mechanic, you may end up getting a Mechana Initiate for free.
There are Promo cards, and perhaps from regular sets where you get bonuses from playing Mechana cards/heroes, 1 of each faction, etc.