Basically, caching allows you to cut your costs if you do it right. Also it is worth to note after 12 months API Gateway stops being free and caching may decrease amount on your bill. However, caching cluster is paid on hourly-basis and you must know if it will be worth to use it.

Personally, I don't imagine to provide aaaaaaaaa.execute-api.eu-west-1.amazonaws.com/v1/transactions/XXXX/cancel as a API endpoint in the documentation of some product. Well.. It'd definitely made my day if I will see such endpoint in i.e. Stripe docs. Everyone uses short like address like api.example.com so there is definitely use for custom domain name as a feature of API Gateway. Custom domains allows you to separate an API by base paths (i.e. Transactions API, Notifications API, Refunds API) and it easier to upgrade/shutdown... basically maintain your API. Also if you are interested from requests made in two AWS regions and you also care about latency regional endpoints might be way better. Of course, if you will use it with WAF and CloudFront you have a lot of things to configure, which for some companies might be important.