Further, if we supppose as you suggest that various professions will once again become skillful professions with all the complexity and variety that entails, say the profession of Master Sewer, the question still exists why should you put hard work into become a Master Sewer when it's easier to just be a Seamstress since the reward will be the same. As a communist I guess you believe the personal reward people would get from helping others and developing their capacities would be enough, but for something that takes literally years of sustained study and effort I just don't see it.

Any society that compensates brain surgeons the same way it compensates flipping burgers is not going to have brain surgeons very long, whether the compensation is monetary or otherwise.

You're making the mistake of assuming that doctors or any other difficult to learn trade are becoming so simply because of the rewards. This is simply not true as it's far more likely that they become thus because it is their wish to help people or something to this extent. If people did choose their profession according to their income, then we would be seeing far less doctors and brain surgeons.

In any case, any profession can just as well be as skilled as a surgeon, from cooking to sewing to IT. Do not take for granted the current drive of capitalist enterprise to deskill humans and turn them to a simply automaton. It's far more likely in an Anarchist society that positions such as "flipping burgers" will be dismantled and replaced with something humane which has as much capacity for skilled work as any surgery.

To answer your question as it should have been put forth. Yes, a master cook might be just as skilled as a brain surgeon

Furthermore, people do not choose to become a Seamstress rather than a Master Sewer. Those two are part of a scale and the former will become the latter in time as long as this progress is not blocked via hierarchical institutions. As such, you can easily expect people to become masters on their chosen craft as they progress with their lives. This will only be something natural and not necessarily something to be rewarded extra. This is because those who are masters used to be apprentices once and then they were supported by society as a whole (for example by having an equal pay) while they were developing themselves. Now that they are in a position of mastery, the extra productivity they give back makes up for this which to me sounds only fair.

As for jobs that do not take equal skill, those as per the original quote, of course equalize with the fact that people are not equally skilled either.

Finally, you have to remember that I am for abolishing money altogether, so speaking about "rewarding everyone the same" does not make much sense in a moneyless economy.