This is a good behavior, since it means less bytes to transfer per connection. Worst case scenario, the browser doesn't have/can't get the intermediate certs required and the connection fails.
I understand this behavior from a "make the spurious user bug reports go away" perspective, but it's still pretty gnarly :-)
Imagine a junior admin who installs a new certificate (without the intermediate). Tests on their Chrome which happens to have cached the intermediate, validate LGTM and moves on.
Meanwhile it gets deployed and some portion of the site's users don't have the intermediate certificate cached = dungeon collapse.