Well let's start by noting that there are exceptions to this rule. A principal engineer in a couple companies I've worked for was in a higher bracket than almost all the managerial levels.

Next let's explore the ideal case. An engineer is very good at using tools to accomplish work. A good manager should be very good at using/making/helping humans accomplish work. Totally different skill set, but not easy, and potentially very profitable for the company. I think that there is a belief that if you assume responsibility for a team that you are now the primary locus of work getting done or not and thus your risk/reward levels are increased.

The reality is more along the lines of, "persuasive people end up in control of capital and then pay people like themselves more." Really effective leaders, through myriad strategies both good and bad, manage to take the potential work output of a group of individuals and focus it on their goals preferentially. This is super powerful. They see this as their particular talent and power and, noting how powerful it is, want to compensate others who are doing something similar. This is an admittedly jaded and machiavellian take on management.