Explain why it's impossible for the graph with degrees (n-2, n-1, ..., 1,0) when n is greater than or equal to 2 without using sequence algorithms

Question

It's pretty obvious why it doesn't work using the sequence algorithms.

So the way I thought of it:(n is the number of vertices)

at n = 1: you get 0, which is the graph of just one vertex

at n =2: you get 1, 0 which is two vertices with one having a degree of 1, but the other vertex has no edges so this is impossible.

this continues on for n greater than 2 as well. Not sure if this is enough to answer the question.

Edit: possible new solution, there are n possible degrees for n vertices which is impossible when $n\geq2$