In theory, PCI only requires you drop TLS 1.0 "to safeguard sensitive cardholder data during transmission over open, public networks" and for "all non-console administrative access." So an argument could be made that things like static images aren't subject to the 'early TLS' prohibition.
In reality, however, TLS configuration is a per-server/application issue. If your site is serving both sensitive and non-sensitive content, you can't negotiate early TLS based on request type, because the request only comes after TLS has been negotiated. And with HTTP/1.1, for example, you can have a connection which pipelines multiple requests, all of which are under the same negotiated TLS. You can't really negotiate early TLS and then accept or reject requests based on their sensitivity. And even if you could, if it's a POST request sending you PAN data, the damage has been done by the time you get to see the request.
So you're going to find that ASVs require site-wide removal of early TLS for any site that has sensitive content.
Personally, I think you're going to find that the early TLS prohibition is going to flow out to cover all hosts and services, internal or external, sensitive or not. Because the ASV doesn't want to be reviewing individual cases and saying "Oh, you're right, that's the ILO interface for your coffee machine, it's okay if that's got TLS 1.0, because it's only coffee." When SSL 3 got prohibited a few years ago, my experience was that it got stripped out universally.