I don't think randomness is necessarily a bad thing. The only exceptions are (imo)
1) it currently makes it nigh impossible to get a good quanta balance in decks using 3+ elements (except rainbows which use quantum pillars).
2) "Fat" decks, those with more than about 30 - 40 cards, are at a serious disadvantage to leaner decks most of the time since the more cards there are in a deck, the more likely you are to get a hand cluttered by useless copies of cards that aren't needed yet.
I don't think changing the game mechanics directly is the right approach though.
-The quantum balance issue can probably be addressed fairly easily by giving alternate pillars / quanta source cards
-The "FAT" deck problem may be a little trickier. What they need is a way to dig through clutter to get to the cards they need. But this goes beyond the problem of just a bad initial draw and has more to do with the increase in chances of getting long strings of unneeded cards as deck size increases. Its just a fact of probability. The more stuff you have, the harder it is to get to the stuff you need at the time that you need it. Redrawing a few cards in your starting hand probably won't be enough.