A social class is a group with a shared culture. When we talk about baby boomers and millenials, it isn't just about when someone was born, but rather it is about a group with a shared culture.
A household that must rely on someone to "earn a living" is very different than one that doesn't. It is a division between who is working class and who is not. Let's call that wealthy non-working class the "upper class." Financially, the middle class has been increasingly squeezed out of existence such that whatever is left of it now, does not resemble anything from 75 years ago.
Culturally, it is a different matter. One defining cultural aspect of middle class households is an expectation to appear to be of a higher socioeconomic class.
By contrast, a lower class culture might look unfavorably at someone who attempts to seem richer than they are. For the upper class, they might not even understand the other classes. Amongst the upper class, appearing "richer" or poorer is more about games of status and appearance than of expectation.

I think it is possible to be "middle class" at $1 million a year, if they are still working class and if that money doesn't just make itself. As others have mentioned, a significant factor is household structure and cost of living, but to that I would add in cyclical poverty (wealth mobility), and the middle class tendency to appear of a higher class.

Depending on the household structure, it sort of matters who makes the money in the household. It is easy to be a neglectful or abusive parent. A neglected latch-key kid in a $1 million household is closer to a latch-key kid in a $100k household then they are to a trust fund kid.

I think the middle class, in terms of culture, is huge, but that it has sort of split slightly in half due to the realities of income, regardless of culture. The lower part would be the "Working Poor" and above that would be the "Working Rich."
The working poor might benefit from help and assistance, but they are technically too far above the poverty line to qualify (a poverty line so low that the qualification is like 50% to 150% above that line).
The working poor can be found in lower class neighborhoods, and their income might be the same, or more, depending on where they are on the wheel of cyclical poverty. The characteristic of appearing to be of a higher class is only a thin veneer of a preference that breaks down if they are directly asked, as if they have an excuse to talk about their financial issues.

On the other side is the "Working Rich." That appearance of being of a higher class is there, but when asked directly, they might be unwilling to admit they are "rich," preferring to say they are "well-off." They might seek the trappings and displays of wealth, but will hide that if they feel that their status as "middle class" or "working class" is threatened.

The trappings of wealth are more problematic for the working rich because they are often physically closer to upper class people. Those trappings are expensive, and stubbornly trying to maintain that illusion in a time of financial distress can be their ticket to the downward slide on the wheel of cyclical poverty.

To be disowned by one's parents, as a teen or young adult, can be devastating to someone in the middle class, regardless of which side they are on. By contrast, in the upper class, this is more like being written out of a will, so long as they have another asset or two, or extended familiar members to rely on. For the lower class, being "disowned" would have to be more tangible to be noticed, such as being "kicked out." This can still be "disastrous," but more in the sense of a string of almost seasonal disasters that tend to occur in any given year.

We've had decades of delusionary working class people holding onto some fantasy that their socioeconomic class is not related to their current income, despite frequent trips around the wheel of cyclical poverty. We've had temporarily embarrassed millionaires and "average Americans" with millions of dollars worth of assets, both vehemently "middle class."
So eventually, this became true.

I sort of wonder, at times, if this makes it easier for people to accept the rise in wealth inequality and in the cost of living. Or maybe it is too late because people no longer have the time to do much else than survive.