After all, a perfectly balanced game is this:
Everybody roll 1d6. Highest roll wins.
Fun, eh?
How do you feel about balance?
I feel you've left me nothing to vote on in your poll.
Balance isn't everything, but if it is lacking, it can be crippling to your game. Your fortune mechanic is potentially crippling to a game as well, something very like it was used in Space 1889 IIRC, but it's less crippling than poor balance.
The reason your fortune mechanic could be crippling is that it is has no granularity, and can poorly cope with changes in difficulty and skill. As such it can be hard to use it to mechanically define a role for the player, or to provide any sort of character progression. But in a game that isn't intended to go for very long, a simple fortune mechanic like that might not be a problem.
Imagine you are playing a martial arts computer game - lets call it 'Karateka'. Initially, you are amazed by the smooth animation and the apparent depth of the combat system. You can make high, low, and side kicks, straight punches, upper cuts, and body punches. You can make blocks. You can assume a fighting stance, run, bow and so forth. And the game is different than a lot games you've played, in that once you commit to an action, you have to finish it before you can do anything else. So you have to plan ahead. And your foes have the exact same moves you do. You have to out think them. Wow this is cool. Wow this is so challenging. This goes about three screens and then you make a realization.
All the attacks take the same amount of time to make. There is no advantage to a punch. The attacks can all be rated by range. Your longest ranged attack is a side kick. If you throw it, the enemy will either block, throw there own side kick resulting in both sides blocking, or be hit by the attack. There are no other outcomes and no way for the enemy to move through your kick range fast enough to throw another attack - which wouldn't matter anyway because all attacks have the same speed. The whole game comes down to throwing a series of side kicks continually. After some initial experiments, this proves trivially easy to do. Every one and a while you get attacked by the bird, which might require a high kick, but the bird is just another timing problem. There is no strategy to it.
There is literally no thinking involved in the game at all. It's harder to figure out that you need to stand and bow to the princess than defeat any part of the game. Once you figure out the 'secret', you go from struggling to finishing the game in a 40 minutes of continuous side kicking.
Poor balance is like that. It's like opening a 500 page RPG, ogling excitedly all the options and all the characters you could create, and then realizing that the rules are such that you either could play a character that rolls a d6, or you could play a character that rolls a d20. All the complexity is trivialized and smoothed over. The rules might as well be 15 pages long, and have just a single character option. So you ban the d20 character, and in doing so you vastly improve the game.
Unfortunately, in the real world, you rarely can fix the balance that easily.
Is balance everything? No. But it's foundational.