Having a card always do the same thing works better in random opportunity games like Race for the Galaxy or Magic. If you removed all randomness from attacks and defenses in Mage Wars, I would worry about it becoming too Chess like and deterministic. I often object to random outcomes in games, but the damage dice in MW are low enough variance that it doesn't bother me here, particularly with the level of control you have over everything else. Overall I think the random outcomes work well as implemented in MW.
Just to be clear, I'm not arguing that Mage Wars should change the random nature of its combat. It's far too late for an overhaul that large; that ship has long since sailed. But I do believe that the game would have been better if it had lacked such randomness from the get-go. I'm actually not that annoyed with damage being (slightly) randomized. I can tolerate it, although I still dislike it. I view it as far worse that secondary effects are random (Push, Stun, Burn, etc.). Those things can have a far larger immediate impact on the game, and there aren't enough of them in most singular games to even out the distribution of successes and failures. I think a small part of the reason people rely on Teleport so much is because no one wants to risk an entire game by betting that Surging Wave will actually push the target. Even Jet Stream can fail miserably when you need it most.
However, I also acknowledge that this particular issue is a matter of personal opinion. There is no correct answer. If I had to guess, card gamers are more likely to want a deterministic approach, whereas board gamers are more comfortable with systems involving luck. I just don't think luck encourages a good competitive scene. Furthermore, I think your fears regarding the game becoming too deterministic could just as easily have been applied to the decision to remove card draws and simply give players access to everything at all times. Sure, as a result of that, players typically perform a standard variety of opening moves. But the game still isn't anywhere near Chess-like. If combat was less random, the only major thing I could see changing would be a more strategic use of cards (using Arc Lightning instead of Lightning Bolt to kill a dangerous creature with low health, etc.). Players have so many options available to them that there will never be a single set of specific, optimal strategies.
As for playtime, that's mostly a problem for new players. I've played 3 games in 3 hours on several occasions. Playing a single game is hardly as big a deal as you're describing for experienced players. Now, finding people to play with may be a much bigger problem than finding the time to play, but that's a separate issue.
True, play times can be 40-60 minutes. But it's very dependent on which Mages are picked. If you've got an female Warlock vs a male Beastmaster, then the game is probably going to be fairly short. But god help you if you end up in an equally matched Priestess vs Priestess fight with no time limit.
Without a random element introduced you get a "dry," predictable game where the only unexpected outcomes are from the players. Also, if damage was dealt directly without dice rolls and players got to pick which cards they would get to play every round the games would either be over the moment we saw the first card played or games would drag on til the last card is played.
Isn't the first part already largely true? Two of the biggest parts of Mage Wars are constructing your deck and guessing what your opponent plans to do. In both aspects, the players are doing all of the work, and all unexpected outcomes are already a result of their choices. And if both players can objectively tell that a Deathfang is going to lose against a Timber Wolf without any outside interference, so what? That kind of stuff already happens to a lesser extent. But that doesn't matter, because that's not what the game is really about. The game would always stay unpredictable because the core of the game is responding to your enemy's moves with counter-moves that you hope he/she won't predict or be prepared for. The famous words of Helmuth von Moltke are very applicable here: "No battle plan survives contact with the enemy." If you are trying to turtle as a Priestess and your enemy drops a Deathlock, whatever previous plan you had goes right out the window.
Finally, if you think that the random rolling of damage and the effect die are too much for you try calculating the likely chance you'll deal a certain amount of damage with X amount of dice. Now try to compare that to "60!" (or 60 factorial). This is the number that determines you getting the exact outcome you're looking for in a 60 card deck such as in magic.
This is kind of beside the point, but you're slightly overestimating how much luck is present in MtG. Games like that typically have you start off with 7 cards (as well as a potential re-draw), so the likelihood of drawing the card you want is already (very) roughly 15%. Depending on how many turns the match lasts, you have a decent probability of drawing at least a third of your deck by the end. Considering you can have up to 4 copies of the same card in a deck (and it's assumed that players will include multiple copies of extremely key cards), it actually ends up being fairly likely that you'll draw a specific card that you want. What you're referring to seems to be the odds of drawing a card at exactly the time you want it, which is admittedly much lower (and players therefore need to be flexible). Regardless, I'm not arguing that Mage Wars isn't an improvement over MtG in this regard. I'm arguing that it could have been improved further.