We recently ran across someone who was remaining on an unsupported version of PHP because their WordPress theme wasn’t compatible with a newer version of PHP. They didn’t have to do that. WordPress themes can be updated to support newer versions of PHP. If the theme is still supported by the developer, they should be releasing updates to address that. If you are using a theme that isn’t supported by the developer anymore, someone else should be able to handle addressing incompatibilities with newer versions of PHP.
How easy or difficult it is to make the theme compatible will depend on if the theme is extensively using PHP functionality that has been removed in a newer version of PHP. You usually have plenty of warning of that situation, as the functionality will be depreciated before it is removed, so addressing any depreciation warnings will avoid having the theme break later on.
If you are unable to handle making a WordPress theme compatible with newer versions of PHP yourself, we can help you with that.