Promoting the general welfare would require a standard.
Still, both sides support the center, the Constitution. The difference is interpretation. The problem is partly that, as I've seen, some people are immediately upset by the very use of the term 'interpretation' when associated with the Constitution.
Could we say that the 'right' is really the center and that the 'left' wants to liberalize Constitutional authority/central power? 'Right' supports central power and 'left' supports eccentric power?
The Constitution is no more the center than was the monarchy. They are the authority.
Social evolution is the center.
The left seeks it by challenging the authority.
The right suppresses it by appealing to the authority.