Is it only out of sheer luck that all my "txid"s are unique? How should I handle multi-vout transactions?
Why has none of them ever used more than one vout?

If each of your transactions only sends Bitcoin to one receiver, then there's going to be only one receiver output in each of those transactions. Hence you only see a single vout per txid.
You can create transactions which send to multiple receivers. You should see multiple vouts for those. You can make them by using the sendmany command or by clicking the Add Recipient button in the GUI.

And what happens the day this happens?

Nothing should happen except that you will see multiple txids with different vouts. In the end, it all depends on your software and how it is handling that. Since it sounds like you have dealt with the uniqueness constraint correctly, nothing should happen.

Why can't Bitcoin Core just clearly list the human-relevant information instead of exposing internal mechanisms to the &quot;end user&quot;/programmer?

If you want human relevant information, use the GUI. The RPC interface is intended for developers and advanced users. The whole point of the RPC is to allow people to build software that use Bitcoin Core and they are going to need to understand and access all of this additional information.