Upon clicking 'View All' I'm opening a new related list using 'e.force:navigateToRelatedList' in a Lightning component. This displays a 'New' standard button to create a new record for the corresponding object. Can this button be replaced? or removed?
Your ask looks similar to Ideas posted on IdeaExchange.
Similar thread: https://developer.salesforce.com/forums/?id=9060G000000BiS6QAK
This Standard button is not available for overriding or replacement or removing as of now.
You can even create a new Idea for this particular feature, which may get considered/delivered by Product teams in future releases.
Reference to Post new Idea: https://trailblazer.salesforce.com/ideaSearch
The other way of achieving this is to create fully custom record detail page or Custom related lists using code and there you can make use of your lightning component(for 'View All') to achieve the business requirement.
However, its always recommended to make use of Standard components as much we can since, it would add up to performance as well as many factors alongside.