However I would think if one partner earns significantly more than the other it would make sense for the lower earner to have to take on a bit more if you’re working together as a team
I am also baffled as to how you think this statement makes sense or is in any way fair. What you are basically saying is that if Parent A earns 100k for their 30 hr a week job and Parent B earns 60k for their 45 hr a week job, it makes sense to you that Parent B takes on more work! Which is shit for Parent B. It’s a pretty entitled way of thinking.
If you are truly working together as a team, you sit down and work out who is going to do what. Even if that discussion means you are going to book in vaccinations and he is going to take out the bins - and once you have established who ‘owns’ which job you don’t nag, interfere or query unless the other partner seems to be struggling then you ask if they need help. But if you are working equal hours in your jobs, you should be putting equal hours into running the household and childcare responsibilities. If you are bothered by doing all the child-related jobs, offer to do all the non-child jobs such as putting the bins out, managing household finances, DIY tasks, etc.
In our household I do do all the child related tasks (yes, even on my highly paying job, the horror!) but I have no idea which electricity company we are with, don’t get involved in ensuring we are on the best mortgage deal, never put the bins out, and haven’t touched an iron in decades. DH has no idea how the kids got into school or where their uniforms come from, has never taken them to the hairdressers or dentist, and so on. What does make sense is for someone in the household to be responsible for each task and to ensure that task is done properly. It would be madness for both of you to waste energy and time on both becoming familiar with the same task.
Btw I am curious to know what area you work in where you need no apparent people skills at all. I work with just one other person in a locked box 6 miles above the ground and I need people skills more than you might ever imagine!