RFC 6066 specifies that you can only have one certificate in an OCSP response - as with intermediate certs you need to be able to respond with a chain, this does not work. RFC 6961 defines a multiple response capability, but my understanding is that currently this is not sufficiently widely implemented to be useful yet.

Thanks! I thought it's enough if the stapled response contains information only about the intermediate cert, and the browser would accept that as good enough, if the chain it got in the handshake is valid.

https://bugzilla.mozilla.org/show_bug.cgi?id=611836 - this looks pretty abandoned (last comment 3 years ago) :/

and I found no bug for Chrome.

Chrome, as far as I know, does not do OCSP - https://www.imperialviolet.org/2012/02/05/crlsets.html