That's not true. They do, but you have to add it to the Vary header: https://developer.mozilla.org/en-US/docs/Web/HTTP/Headers/Va...
This way user-agents know that the Accept header is involved in the final form of the response. (As another example, Firefox also doesn't take Accept into consideration when caching locally by default, and it does with Varry: Accept)
Their documentation specifically mentions Vary as non-functional[1] outside a paid plan, and even then only for images[2].
[1] https://developers.cloudflare.com/cache/concepts/cache-contr...
[2] https://developers.cloudflare.com/cache/advanced-configurati...
A Vary field containing a list of field names has two purposes:
1. To inform cache recipients that they MUST NOT use this response to satisfy a later request unless the later request has the same values for the listed header fields as the original request (Section 4.1 of [CACHING]) or reuse of the response has been validated by the origin server. In other words, Vary expands the cache key required to match a new request to the stored cache entry.
[...]
When a cache receives a request that can be satisfied by a stored response and that stored response contains a Vary header field (Section 12.5.5 of [HTTP]), the cache MUST NOT use that stored response without revalidation unless all the presented request header fields nominated by that Vary field value match those fields in the original request (i.e., the request that caused the cached response to be stored).
Notice that this is the HTTP "Semantics" RFC, not the "core" one (Message and Syntax) which is the venerated RFC-7230 [1] which is indeed quite simple for such a widely used protocol.
This RFC only defines a handful of "header fields", almost all of which necessary for actually being able to "frame" (find the beginning and end, applying decoding if specified) the HTTP message : https://www.rfc-editor.org/rfc/rfc7230#section-8.1
Yes, I know (and personally experienced) that most clients forget to include "Vary" field, or don't know that it exists, or the problem that this header solves exists) but when they do include it, they actually mean it and rely on it being honoured, one way or another.
PS. By the way, 7230 is obsoleted, you're supposed to use 9112 now.