Let's say someone goes into strategic AI research at the Future of Humanity Institute because this is proposed to be one of the most impactful career paths there is. In aiming for that career this person relied on the labour of several teachers. When the researcher is sick, they rely of the labour of doctors...

This doesn't seem to pose so much of a problem if you are trying to rank what is most valuable on the margin. Suppose every human activity is dependent on having at least one doctor and at least one farmer producing food, such that these are completely necessary for any other job to take place. It doesn't follow that we couldn't determine which job it would be most valuable to have one additional person working in. For example, if we already have enough doctors or farmers, even if these jobs are entirely necessary, we could still say that it is more valuable for a further person to work in a different field.

I think you've basically captured this with your artist example, although it's worth noting explicitly that how important art is on average, is different from its value on the margin, i.e. we could think that art or being a doctor or whatever, is the single most valuable human activity (on average) and still think that it would be more important for a particular person to go and work in another activity.

I'm not particularly EA, but I think they gist of the argument is - you should work where can you make the most marginal impact, not necessarily in a job that is the highest impact overall. So if you're choosing a career for impact, you might be one of only a few thousand people thinking about things in EA terms. If you want to have a large impact, then you ought to look at things that are large in scope and neglected, etc.

If somehow the EA community coordinated all resources, or was much much larger in size, the recommended careers would probably be different. In that case, obviously some people would need to be teachers, farmers, etc., and it would be important to encourage people capable of doing those things well to pursue those careers. But, given that there are relatively few people willing to change their careers for this sort of impact right now, the careers recommendations that are made in fields where a few people might have a larger impact.

This isn't a denial of interdependence. It's more of an implicit acknowledgement of the limits of the current size of the community.

Another factor is that many careers that EA careers are dependent upon are likely to be filled regardless. There are people who would like to be, or whose circumstances cause them to be, teachers, construction workers, farmers, truck drivers, etc. So while all those jobs probably have a (positive) impact, it's less urgent for someone who wants to have the greatest impact to pursue that as a career. While education might be important, I know that if I don't apply for a job at my local high school, another (even more) capable teacher probably will. Instead, on the margin, an EA might have a greater impact by pursuing something more neglected, or pursuing a career where they can earn money to donate to a charity that can hire more people for a neglected cause, etc.

The core idea is that because there is only a small community of people interested in having the greatest impact they can, then they should pursue careers that on the margin would be most likely to have the greatest impact. It doesn't necessarily mean that these careers are intrinsically or functionally "better" or higher ranked than others. They are prioritized by EA because few people are in EA, and fewer people are thinking about pursuing recommended careers.

I think the other responses capture the most important response to your question, which is that we tend to look at the value of things on the margin. However, as you're clearly thinking intelligently about important ideas, I thought I'd point you in the direction of some further thinking.

Another, perhaps clearer case where this "thinking on the margin" happens is with charity evaluation. If, for example, there existed some very rare and fatal disease which cost only pennies to cure, it would be extremely cost effective for people to donate to an organisation providing cures, until that organisation had enough to cure everyone with the disease. After this point, the cost effectiveness of additional funding would dramatically drop. Usually this doesn't happen quite so dramatically, but it's still an important effect. It is this sort of reasoning which has prompted givewell, for example, to look at "room for additional funding", see here.

There's another way of looking at your question though, which is to re-phrase it as "how should we assign credit for good outcomes which required multiple actors?"

One approach to answering this version of the question is discussed in depth here. I think you may enjoy it.

I have heard some people wanted to have a 'high impact career' but instead they became a 'stay at home mom or dad'. They had to raise 1 or more children--who then went on to become noble prize winners. That to me is an 'interaction effect'.