Thanks for the response, and for explaining the underlying philosophy. A shorter follow-up / response:
I do think there's value, even for more complex hardcore games, in keeping the basic game simple. Also, for the purposes of teaching new players the game, cards and decks which are mostly comprised of plain and straightforward conditional damaging cards are a good thing; it helps retain the 'easy to learn' part of the ideal 'easy to learn, hard to master'.
I like the idea of cheaper cards and permanent effects; I think that might help create actual decision-making in the earlier turns. Needless to say, with the current health amounts and duel rules, cards probably need to be weaker if they're cheaper or duels will just be even shorter. (triple Tender Kiss on turn 2 for 2+7+7 = 16? The horror...)
It would, on reflection, be unreasonable of me to expect the kind of half-hour gambit-pileups or puzzle-like control battles that Yu-gi-oh sometimes produces from a game like Sapphica, and that's not really the theme of Sapphica anyhow. And actually, thinking about it, 5-minute duels sound perfectly fine; my problem is (as I'm guessing you already figured out) with 1-minute duels (not exaggerating; out of curiosity, I decided to test it, and I can consistently win with Fingers Do The Walking in under 60 seconds, on the 5-mana turn*) where I know what card I'm going to play next before the opponent even takes her turn. Might be important when talking about duel length to bear in mind that there's no turn timer and different people play at different speeds, especially with 18+ games, so it could take someone else 5 or 10 minutes to play the same exact duel I can finish in 1 or 2.
A couple of interface related suggestions I didn't think of before because I was tired. These would also be more important if I ever played more than 2 cards in a turn:
1) Add a display for the current Grower bonus, or make still-active cards stay up on one side of the screen, or something. Similar for Heal Chain. Or maybe somewhere you can click or hover over (maybe the "health bar"?) to display active card effects... basically just make it so you can see every card that's currently affecting the game. This is probably extra important when cards with persistent effects are added. (The way Invest is currently displayed is fine.)
2) Indicate somehow whether a Chainer card has been played this turn: Maybe a visual indicator (a tick, or a chain icon, or a glow around the edge, or something) on other Chainer cards, or just in a corner of the screen. Or maybe some sort of action log would be better? Or a discard pile could perhaps work... or, like with the Grower suggestion, the first Chainer card played could stay up on the screen until the end of the turn. Chainer feels to me like more like an effect that's printed on the second card, though, so it's likely the indicator should be on the second card as well.
* Test game: 3 damage turn 1 (Finger Bang); 4 damage turn 2 (Helping Hand); 3+5 damage turn 3 (double Quick Draw); 5 or more damage turn 4 (there is no 2-card combination in the deck that doesn't do at least 5 damage, but you can do up to 8 with your 5 mana, making up for a weaker turn 3 if you only drew one Quick Draw by then, or had to use lube on turn 1, or something).