Can you use BGP to connect to the global Internet without having a public BGP AS number? Of course, assuming your Internet Service Provider is willing to run BGP with a network using a private AS number. But what happens if you want to connect to two ISPs? It’s ridiculous to expect you’ll be able to persuade them to use the same private AS number.
That’s one of the many use cases for the local-as functionality available in most BGP implementations. You can practice it in the Use Multiple AS Numbers on the Same Router lab exercise.