This turned into the longest thing I've written in ages.
You gave quite a good explanation, and there are just two big points I want to add to it. Sorry if I get basic with it or seem condescending, but I'm also writing with new people in mind. The first point is that liberal capitalism is capitalism that is not yet fascist, and the second point is that for anyone living in one of the many places the west exploits, it already is fascist. Because of how writing this shook out, I've tried to make these points in the opposite order, because it's easier to follow that way.
Nothing is static, everything is a process. A mountain is the process of plate tectonics, an animal is the process of cellular life, and a capitalist economy is the process of accumulation. It outcompeted and replaced feudalism, a more primitive form of accumulation. Every form of social organization has inherent contradictions, inherent tension points where the interests of one group pull against the interest of another. Peasant vs landlord, yeoman farmer vs slave, industrial worker vs factory owner. These roles are defined by their relationships to the means of production and to each other, and when conditions make those relationships untenable, they break, and a new dynamic arises. For example, when the conditions of defeat in the Civil War but also a paltry reconstruction effort by the US made chattel slavery an unviable arrangement for the wealthy, they started up the sharecropping industry, a form of wage slavery the new government found acceptable. Obviously prison slavery also started ballooning afterwards, and now we have more prisoners in a larger carceral system in the US than anywhere else on Earth. The profit margins of chattel slavery were stabilized by other types of slavery. Because a capitalist economy requires infinite growth, it requires new frontiers to exploit, places where resources and labor can be had cheaply and sold for more elsewhere. In US history, these frontiers (and the wretched economic conditions necessary to extort cheap labor) have always been enforced by military and intelligence organizations. Look into the history of any country the west uses for cheap labor, cheap materials, or as a trash dumping ground, and you'll find a history of naked imperialism that set the conditions for all these "voluntary, free market" transactions that always seem to screw over anyone who isn't part of the so-called first world.
The need for profits drove colonialism, it drives neocolonialism today, and when one frontier closes, another must open. If no external frontier can be opened, it will be an internal one. Fascism, economically, is is the attempt to open up an internal frontier against a segment of ones own society. It's capitalism in crisis mode, a rampant imperial economy that has begun chewing at it's own flesh to make up for the caloric deficit. This is the stage at which decline will be felt by the people living inside the empire, with things like infrastructure failures, mass poverty, mass incarceration, crimes of desperation, an explosion in new cults, and outbreaks of disease becoming commonplace. These conditions are symptoms of the contradictions between the classes becoming irreconcilable: decades of austerity, of public funds and programs being looted by the wealthy, of endless imperial wars, of the privatization of every industry and resource, even vital resources like food and water that people need to live. This is where we're at now-and I havent even mentioned the concentration camps.
Looking at it from a class perspective, these are conditions that the American and westen bourgeoisie have inflicted both on the proletariat of their own countries, and to a much greater extent on the rest of the world. The people of all these countries we ruin don't choose fascism, our ruling class chooses it for them. The people of America don't choose to go to war, or for healthcare to cost a million dollars, or to give the police tanks and combat robots. Our ruling class chooses it for us. We don’t actually live in a democracy, we live in a dictatorship of the rich.
When we consider that a capitalist economy has only one goal -to accumulate capital, to make fewer and fewer individuals richer and richer- and that it will fufill this goal at any cost and when we consider that extreme fascist policies are very good for private accumulation, it leads to an uncomfortable conclusion: that any liberal capitalist economy, after exhausting or losing access to it's external frontiers, will inevitably become fascist, must inevitably become fascist, or be outcompeted and absorbed by a more ruthless competitor.
As long as capitalism is the dominant mode of production on this planet, fascism is it's only logical endpoint.
TLDR what we think of as liberalism is actually just when the fascism is contained in the countries we inflict it on.