In most card games I've played, there were heroes for every faction that had their own passive ability that would some what define the strategy of their deck, I suggest that for this game to add more of a strategical outlook. Though it may seem powerful, every one would have one and by that, everyone would be powerful.
Examples, specific heroes based on your faction & sub-faction combination;
Mono Swamp; When a minion dies, deal 1 damage to opponent.
Mono Air; When you play a spell, a random minion you control gains Quick, and 1 Strength(Or Health.).
Fire|Forest; When you tap for power, a random minion you control loses 1 Health, and gains 1 Strength.
(I have a really good one for Ice|Underworld, but I'm not sure I should spoil Ice right now.)
Though some ideas may not be focused towards.. what an actual major strategy can be, at least it's something.
Next, I'd like there to be no faction restrictions when not using minions in deck building. You can make really neat decks without minions if you could mix more than two factions. Possibly a Barrier-Stall deck. I tried that with jungle and air, and use a tornado with razor weed to give me infinite razor weed in my hand, maybe even possibly no faction restrictions when using a certain type of minion (Mage/Mancer. Dragon. Kobold. Fae.)
Now to combine both ideas;
Dragon as only minion-type(Dragon Master); Dragons you play gain 1 Strength and 1 Health. (I find it slightly fair, considering people's possible ability to counter these, as well the difficulty to obtain the dragons.)
Kobold(Kobold Enslaver.); Cards you get from Kobo's cost 1 less.
So that's it, I don't know what to expect, other than a 99% chance that the ideas will be rejected, or "considered.". I know Goblins, it would take a while to even think about implementing these ideas.
There are several reasons we had a 2-factions-per-deck limit.
(i) To keep the flavour of the factions, so decks don't become multicolour generic designs
(ii) To avoid the issue of players cherry-picking the most abusive combinations across all colours
(iii) As there are no mana/land cards, so it would be just as easy to field a multicolour deck as a single colour i.e. there would be no disadvantage as compared to a single colour deck.
Your idea of hero cards is quite possible. Something like a Kobold King would be feasible yes. But any card that references cards of its own type, giving them some bonus, is pretty much one of these card types already.