It also makes absolutely no sense for the institute to use caps as currency.
This is the only caps/currency-based thing that bothers me in Fallout 4.
It does seem illogical that they would accept caps, rather than barter for items, given that the Institute does not trade with other people.
However, the Institute does have operatives outside in the wasteland, and they would be expected to trade using caps.
Therefore the Institute would know that caps are their means of trading with wastelanders.
This means that the only illogical aspect of the Institute and its use of currency is the fact that the requisitions Synth even sells items at all. Obviously when items are normally requisitioned from him by Coursers, they wouldn't need to pay, or have anything to pay with.
The fact that he does exchange items for caps with the player can be explained by the fact that he's given special authorisation to do so.
Accepting caps is also useful, because those caps can be given to Institute operatives in order for them to purchase goods on the surface and blend in.
Of course, Tony wouldn't know any of this because he hasn't played the game.
how often do you encounter power armor and cars powered by fusion in real life?
Also, the answer to his question is, quite a lot.
There's no shortage of supermarkets, bars, restaurants, houses, shops or any other that have a variety of bottled goods that have bottle caps.