Function URLs aren’t part of lambda, they’re just a thin abstraction around API Gateway v2 (http APIs) that allow all calls, and have randomly generated domains, so you’re not gaining anything and losing some functionality by doing this instead of running an API GW with lambda proxy integration yourself. If setting up API GW is too difficult, you could use SAM or Serverless Framework to automatically provision it. Then you can have a real domain, SSL, failover, endpoint validation, etc.