You're not grasping the part where there is material work and labour in most parts of the value chain including maintenance, inspection, and distribution of builds.
Only 15% of that $20 goes to Apple - while that may be a few points to high, it's not egregious.
The rest of that money goes to the person responsible for maintaining the build, which is 'work'.
"That's unacceptable and repugnant, "
This is a completely naive view, tantamount to saying 'People should work for me, for free, because I said so, and it's repugnant for them not to!'.
"what I want to achieve with this free software is that anyone be able to access it without barriers whatsoever, including payment. "
For 'source code' - this is already possible, because 'source code' can fairly easily be provided 'for free'.
But a maintained and up-to-date build, for specific platforms, with all of the unavoidable regulatory overhead - has cost.
If you want that to be 'free' - again you're expecting someone to labour for you.
There's an easy answer to this -> it's $20 on the App Store.
If you want to do free labour and make it free, you can do that.
But otherwise this 'moral indignation' and 'repugnance' at people who are unwilling to labour for you, for free, is a problem.