I would like the standard "New Quote" button to appear on the quote page's list view. It already appears in the opportunity related list, is this possible?

@Michael Reichel Your usecase is pretty unique. Because, considering sales process.. Quote Object has been designed in such a way that, one would start creating quotes from Opportunity related List; since Opportunity data drives quote creation (which is the next step).

In your case... you are asking for New quote button to appear in List View. Its a different usecase and i am curious to know the drive behind this.

Lastly, an approach we can consider is.. 

1. You can create a Vf page which exposes the New Quote standard Button.

2. Then under set up || Object manager || Quotes || Under Buttons and Links.. click edit next to List and View. Override with VF page.

BUT.. be sure if you really want to go this route considering the sales process.