Ok, but the unspent output takes space as well. I think you could just replace it with the fee. Not sure if I'm missing something or if it was just an arbitrary design decision.

It has to do with the way transactions and the blockchain ledger works, reread the transaction part of the article and it might make more sense. Basically, transaction outputs can either be spent or unspent, you can't half spend an output (or perhaps more accurately, you can't spend a previous output twice).

Yes I understand that's how it works, but I don't get why it's important. Surely you could double spend an output as long as you don't exceed its value; and that looks easily verifiable.

Ah, my bad. Sorry if I was being condescending in my previous reply then.

I suspect it was a design decision, yeah. If outputs could be spent multiple times then you'd need to traverse the chain of outputs backwards to see how much an output has left in it. Bitcoin's implementation is less complex and more elegant, imo.