Depends on where you see those headers coming out. You didn't mention.
Everywhere in my /blog/ hierarchy.
See this screenshot Note the expiry date that's 22 years ago...
No other part of my site does this or issue those headers, just the blog. The other parts of my site are either SSI or perl and neither do this.
I know enough about the way apache works to know it wouldn't be issuing cache-control and pragma headers unless it was instructed to so. Neither my perl nor SSI parts of my site do this, so why does WP?
What you're asking me to do is issue a header() instruction to stop apache from issuing no cache headers it *shoudn't* be issuing in the first place. A bandaid to fix a broken bandaid...