A license is permission given by the copyright holder to someone who would not otherwise be legally able to use the content lawfully. Since the holder may freely use his or her own content in any way, a license to oneself is superfluous, and does not bind the owner.
This is similar to the fact that one can put up "No trespassing" signs on one's property, without preventing oneself, or those one invites, from using the property.
Moreover, a copyright owner can grant two or more different and incompatible licensees to the same content. Such licenses can be granted to different people, or all can be granted to the general public. Granting one license does not preclude later granting a different and incompatible license. Anyone who has been granted two or more different licenses may use the content under the terms of any valid license.
Many open source and permissive license, such as CC licenses, are, by their terms, permanent and may not be canceled, except as the law of a particular country may grant cancellation privileges regardless of license terms. (US Copyright law, for example, permits cancellation during a 5-year period starting 35 years after creation or publication, regardless of previous agreements.) But the owner can always grant additional licenses on different terms.
Not all streaming is commercial. An NC license provision would prohibit commercial streaming, but not other streaming. But the owner could always grant an additional license for commercial streaming.
I do not know of a standard public license that permits commercial streaming, but no other commercial uses. But an owner is not limited to pre-written standard licenses. Any owner may issue a license with whatever terms the owner wishes, although in creating one's own license, it may be wise to consult a lawyer to avoid unexpected and unwanted results.