You forgot the most obvious reason: a built-in currency is a verifiable thing that can be transacted over the network.
Yes. Not sure though that that is a separate reason, more a crucial element that makes a built-in currency able to function as a solution to the problems mentioned in the 4 reasons I gave
If the currency is created and issued by something external to the network, how can individual nodes actually verify that the person spending the currency both a) actually owns it and b) has not previously spent it elsewhere? The only way is to require that the person deposit the currency at a specific institution, but that can't be decentralised.
To be sure, there is a difference between saying that the network requires units of something for transactions and saying that those units function as currency units. I'm not asking whether it is possible to do away with built-in units for transactions altogether, only whether it is possible to do away with built-in units that function as currency units.
If we use the ledger terminology, for the slots in the ledger to function as a currency there need to be limits on their supply. But if they simply function as media for transactions of whatever kind (by representing e.g. external currency units, stocks) then those constraints on their supply are no longer necessary and there can be an unlimited number of them. That way, the spots in the ledger still function as the media that make all sorts of transactions possible (by representing ownership of something external to the ledger) but no longer as currency units. And in that way, individual nodes can still verify that the person selling a spot in a ledger (that represents e.g. a stock, or a dollar) actually owns that spot and has not spent it elsewhere.
The problem then however is that in that case they (especially newly created ones) could no longer be used to reward miners, speculators, founders etc or to prevent spam because they simply aren't valuable in and of themselves anymore. Their only value would be derived from the thing that they represent outside of the network.
So the only way in which they could still function as rewards despite there being an unlimited supply of them is if individual units are tied to something external to the network, and yes, then in many cases issues of trust will re-emerge.