Of course art is worth more than a minimum wage job doing some menial task like flipping burgers or ringing up groceries. Art involves the heart and the soul and pouring all you've got into what you're doing!In monetary/economic terms, I have to disagree: the prices of products and services are set by trade; what people will accept to provide them and what people will pay for them. Menial tasks may be worth more than art, depending on the situation. Some forms of art only have value to others at a high level of skill (e.g. singing, dancing), and even if jobs are available at lower levels, they tend to be of a menial and uncreative nature (e.g. animation inbetweening vs. keyframing; sewing fursuit bodysuits and paws vs. designing heads).
In market theory, both sides benefit from a trade in that they get something that's more valuable than what they give up - though one may benefit more than the other. The price is a lower bound on value, not the absolute value. That is, in an efficient market, art might be worth a lot more to the person who acquires it; but if they can get the equivalent for less, they will. Artistic services are no different. Nowadays, most of us are competing in a global economy, and that tends to drive prices down. Live somewhere expensive, like most of the USA, and you are at a disadvantage.
Now, I'd very much prefer to have people engaging their hearts and souls over sitting in the checkout lane. But many artistic careers have low barriers of entry and a relatively comfortable working environment, leading to high supply; while demand is elastic (people don't need art like they need food) - and this in turn leads to lower wages; quite possibly lower than the minimum wage. This may be one reason so many artists are freelancers. In a post-scarcity economy this all wouldn't matter and we would likely see many more artists, writers, etc. (Of course, we could all end up like the humans in WALL-E . . .)
Being fully involved in a task probably won't make your effort inherently more valuable to others, but it may provide a competitive advantage; you'll likely perform better, stick at it while you're learning and not making much, etc. This is true of all skills; I saw people drop out of computer science who were only studying it because they/their parents had heard there was money in it.
tl;dr: You'd charge more if you could, while others would pay less if they could. Each party is trying to get the best deal. That's how markets work - and they don't necessarily value your scribblings over the motion of a mop, no matter how much heart and soul you put into them.