I am paying for the Starz subscription through Roku. Why is it not possible to watch Starz on hotel smart tv's when I am travelling? Why can I not watch my subscription to Starz when I am visiting my son who, also, has a smart tv? I can login to the Roku channel but I cannot to the Starz through Roku. It always asks for my payment information. This is ridiculous that I cannot watch it on other Smart Tv's!!!
Because you chose to subscribe to Starz through Roku, this subscription is tied to your Roku account. When you are not connected to your Roku account, such as when visiting friends, etc., you don't have access to this subscription.
This is not unique to Roku. Subscribing through a third party (Roku, Amazon, Hulu, whomever) you nearly always can only then access that subscription via that third party.
If you want to have access through multiple platforms, you should subscribe directly with that service on its web page. Then you can use and log into that service wherever it has made a dedicated app available.