What’s the rationale behind the HTTP Date header?

Per the spec, it is used in age calculations. If you don’t know what time the server thinks it is, you won’t be able to calculate the “age” of a resource. Here’s the relevant text from the spec:

Summary of age calculation algorithm, when a cache receives a response:

age_value
is the value of Age: header received by the cache with
this response.

date_value
is the value of the origin server’s Date: header

request_time
is the (local) time when the cache made the request
that resulted in this cached response

response_time
is the (local) time when the cache received the
response

now
is the current (local) time

apparent_age = max(0, response_time - date_value);
corrected_received_age = max(apparent_age, age_value);
response_delay = response_time - request_time;
corrected_initial_age = corrected_received_age + response_delay;
resident_time = now - response_time;
current_age   = corrected_initial_age + resident_time;