I disagree. While the terms "lower middle class" and "upper middle class" are perhaps unnecessary, the term "middle class" itself is an important economic (and socioeconomic) distinction, although its exact definition is highly contentious.
Here are my own definitions (it's important to note that sometimes people don't fit neatly into a single category):
Lower Class (also called the Working Class, or the Working Poor): They live paycheck-to-paycheck, usually at job(s) that have low pay, shifting schedules, no benefits, low job security and no possibility for long-term career-building. They own very few assets, if any, and rent/borrow most things. They are usually one medical emergency away from financial ruin (at least in the USA). They are too worried about tomorrow and the next week to worry about further into the future.
Middle Class: These people have fairly stable jobs that have decent pay and benefits. They often build careers around those jobs and it becomes part of their identity, which can be seen in the way they think of themselves and introduce themselves to others (e.g. "I'm an accountant"). They own or make payments towards owning core assets such as house. They sometimes own small businesses. If they lose their jobs, they can use their skills and connections to find another, but it can take some time. They tend to plan and save for the future, at least passively (e.g. 401k accounts).
Upper Class: The upper class is defined primarily by wealth. Even when upper class folks don't have "fuck you money", their wealth enables them levels of comfort that can only be dreamed of by the Lower Class, and is looked up to by the Middle Class. Work tends to be optional for most, and tends to be about prestige and social class rather than a necessity. When they lose their jobs, it's mostly because of corporate politics or some sort of scandal, and they can trivially find another job using their connections (usually an email or phone call is sufficient).
