I don't want to diss you but are you from another planet?
No.
But, it appears you may be.
The invoice number? A Bitcoin address is more like a customer ID, which remains fixed!
You are quite mistaken about that.
A bitcoin address is intended to be used only once and as a method to identify a payment. That sounds like an invoice number to me.
It would be much more convenient for businesses or individuals, to provide their counterparties with fixed addresses for further use.
I suppose it would be convenient to provide "counterparties" with a fixed invoice number for further use as well, but it doesn't make sense and is really quite silly.
Otherwise a new one would have to be created everytime someone sends you a payment.
You mean, like an invoice number? Right. Exactly.
What a nuisance!
Most people don't think of invoice numbers as being a nuisance.
And imagine this is done automatically, and a partial payment is received: CHAOS, CONFUSION and MAYHEM!
Or, you just wait to receive the full amount.
For privacy you would need a new private key every time anyways.
Correct. Each new address comes with its own new private key.
But if you want privacy, BTC is not the right crypto.
Perhaps, but it's better than alternative forms of electronic representation of value (such as bank accounts).
I guess a company with good blockchain knowledge could try and create 1 private key per customer
Any company that doesn't understand that every address has a separate private key doesn't have good blockchain knowledge and shouldn't be managing their own cryptocurrency decisions.
issuing a different address on that key
Not possible. Each private key has only one address.
for the average company/individual that is way too much overhead.
It's too much overhead for a company (or individual) to keep track of what addresses they give out for which payments? Then they probably can't manage money at all. They probably need to get someone else to manage their money for them.
So yes I do think address re-use should be fully supported.
You can think whatever you like. It doesn't make it a good idea.