I honestly don't agree with much of what you have asserted about a two-party political system in this country... Historically, there have always been 3rd parties, and sometimes 4th, and 5th, as in the 1912 election of Wilson's first term... Granted, for much of our political history, 3rd parties have simply not carried enough membership to get their candidate elected, but they have greatly influenced elections by diversifying the electorate...Furthermore, they have succeeded in that they have offered representation for their members who were not aligned with the platforms of the two major parties...
However, in modern politics, it's less likely now than ever that we will see any significant power come from a 3rd party to get a POTUS elected. Very simply, a party's power is determined by the dollar, and the ability to fund raise. For the members, a political party is an investment just like a stock or bond with the desired political outcome being the dividend...
The founders designed our 3-branch system expecting gridlock. This was to be the check and balance on any radical change or one-party dominance... As far as any one party gaining control over the WH and both houses, it has only occurred 6 times in our history... It usually occurs when the other side as failed miserably on collective policy and sweeping change is warranted by the electorate... The "compromise" you mention no longer exists when one party becomes too radicalized as is currently the case with the democrats...
One-party control being a good or bad is in the eye of the beholder... In this upcoming election, I view it to be a very good, and necessary thing especially when the country faces multiple crises and is on the breaking point as we are... For as much as the phrase has been overused in the last 2 political cycles, democracy actually is at stake... Ironically, it's the democrats that are seeking to destroy it, and not the other way around...