My way is fully democratic because you've forgotten you are voting on a list of things, not a single thing.

What you like about list A can easily get traded away after the election by politicians when you have no say.

However is list A has to be approved before an election, then you get everything on that list and you know what you are going to get.

If I elect politicians who are likely to trade away list A then that indicates I either don't value list A so highly after all, or that the politicians are liars. I don't see how your system solves the latter problem - either way the solution is to not vote for politicians after they have proven themselves liars.

It seems to me that in FPTP you end up with both parties trying to calculate the absolute minimum they have to promise to their base in order to get just enough of their vote to win the election by 50%+1. And, after the election, trying to calculate what is the minimum amount of promises they have to keep, without depressing voter enthusiasm so much that they lose the next election. (The Democrats seem especially bad about this, and I say this as someone who votes Democratic and volunteers for Democratic causes and candidates.)

In others words in FPTP you have politicians trying to figure what is the bare minimum they have to do in order to not get fired. These are perverse incentives, and they do not tend to attract the sort of person I want to vote for.

Ranked choice voting seems to go a long way toward addressing this: I simply rank candidates in the order that they match my preferences, perhaps also accounting for their perceived trustworthiness as well. And, more or less, the candidate who best matches the aggregated preferences of the voters will win.