In short, no. You should be able to use streaming services with or without a dedicated IP address, or even a VPN. But if you’re using a VPN to access geo-restricted content libraries for other regions, a dedicated IP address may help.
Streaming services generally have VPN filters, and try to enforce their licensing agreements that restrict content to certain regions – if you’re flagged as a VPN user, the service may redirect you to a version of the platform that only hosts globally available content, if they let you into the platform at all. A fixed, static IP address is more likely to appear legitimate and bypass those filters without issue.