I feel like I have wasted my money buying the Roku stick. As I live in the UK and have to pay for a TV licence to watch live TV, there is no app on roku after hours of scrolling (because it is not searchable) that can list the free live UK channels unless I have an aerial in which case I wouldn't need Roku. Why?
I'm not sure what you're asking here. There is nothing mutually-exclusive between a Roku and a TV connected to an an aerial. The Roku stick is not meant to connect to an aerial but instead streams from the internet. When you want to stream (eg: Netflix, Prime Video, Paramount+ etc.), switch the TV input to the Roku. When you want to watch over-the-air TV, switch to the TV's aerial input.
You can search the UK channel store here:
https://channelstore.roku.com/en-gb/browse?locale=en-gb
For example, I searched for BBC and found their iPlayer app:
https://channelstore.roku.com/en-gb/details/249f43d8f1d06bc38d8b9fb994e302a4/bbc-iplayer
And to add what @Strega2 said, if I understand the UK TV license correctly you don't pay the license fee if you are only streaming on your TV. Any streaming costs are paid directly to the provider, not the BBC (unless of course they are the provider).
If you go to the Channel Store on your Roku, you can find all the channels/apps that are available to you in the UK. Some will be free (usually ad-supported) and some will require a subscription (Netflix and Prime Video for example).
@licencePayer, to add to what's been said, if your Roku account isn't associated with the UK you won't see the apps available in the UK (and you'll get no search).