The current embed functionality is not fully usable in Wordpress due to the default security settings in Wordpress, which strips out any code inserted by non-superAdmins in Wordpress. While there are work-arounds for single site instances of Wordpress, these solutions are non practical for large enterprise multi-site Wordpress instances with dozens of sites and hundreds of users.
I propose that either the [embed] or [video] shortcode in Wordpress be extended to include Stream. This could at first be done via a Wordpress plugin, but once it's vetted, it could be submitted to be added to the default Wordpress core.
This has been done for other services in the past. Currently Wordpress natively supports Youtube, Vimeo, and many other multimedia services via shortcodes, so that model should be able to be followed to add support for Stream.
Reference links at Wordpress: