“Outside of the two coalition parties there is a thin fringe of unaffiliated people. It’s not a broad middle ~ more like a desert.”
I tend to (reluctantly) agree, but I can’t accept the premise that even a majority of the people in the “two coalition parties” have made a considered decision to buy in to the tenets of their party. It seems to me that if there were a way to get people to look past the R or D and see the truth - that they really ARE conservative, that they believe, deep down, in the values on which this nation was founded - that “desert middle” you so aptly describe would be much more densely populated and people would make REAL election-day decisions.
Pollyana out.
Those affiliations ~ kinship, location, friendship, work, economic status, religion, color, height, sex ~ maybe even scent ~ define us first long before we decide if we are Republicans or Democrats.
This is a given.
The American single member district system for discovering fit officers of state simply forces the issue by requiring, ultimately, that you get 50%+1 vote to win!
Your relatives, neighbors, friends, employers and employees, and so forth spend a lifetime trying to get you to make that one last choice ~ POLITICS ~ because they, in their combination of affiliations believe they will benefit from you choosing their way, and even if you don't, you'll still be relatives or friends ~ because we aren't going to give up on you.
The hypothetical 'Broad Middle" cannot exist under those conditions. You will be part of one or the other of the two coalition parties, and if your affiliation group switches sides, you'll more than likely go with them! Even if you don't, you'll be in a new minority.
Way back at the beginning when the Founders set up our nation-state with it's bifurcated government (federal and state), they created competing centers of power which were single-member districts. Throughout American history there have been only two significant deviations from that ~ one was the South Carolina legislature where "county supervisors" were also delegates to the legislature, and depending on population of their home district, they had votes of different weights. The other place was Indiana where the county itself was the smallest district, but with multi-members depending on population.
The result was the same ~ counties with large populations tended toward "Party List Voting"! That didn't give rise to different parties, but factions within the parties were able to push their candidates forward to run with the main party candidates.
First time I voted I had to select 25 representatives ~ invariably there'd be some minority guys in there ~ chosen by someone to be on the list.
If you combined that situation with run-off elections you could probably force those factions out into the open as independent parties ~ which is what happens in European countries with that form of election.
The math is that with two stage voting, and multi-party districts, you only need 2.5% of the vote to actually put a member of your faction into a parliament with at least 25 members!
NOTE: Which kinda explains the koo-koo fringe people found in so many city councils where selection is non-partisan or within just one party.
After convening the parliament, the various faction representatives will tend to coalesce around a "Government" and an "Opposition".
Indiana never went to runoffs but South Carolina and other Southern states commonly held them. You still see reflections of that in the results in South Carolina where it's always been considered "normal" to vote for the man and not the party ~ which puts non-standard politicians in power. If they had to run as a real Republican in Ohio they would never win, but they also could never win as a real Democrat there either!