If a programming language allowed the creation of database tables, but only allowed one field to be used as an index ... how limiting would that be? I am not a real database programmer, so I'm wondering if such a system could be used as the basis for serious databases, or would be only a toy.
That would be extremely limiting. I've seen as many as 11 indexes on tables I've dealt with, all of them having a purpose. No doubt there are cases out there with substantially more.
At a minimum in a database the primary key and all foreign keys will be (or should be) indexed.
Also it's common for indexes to span multiple columns.