This is pretty much how it is in most of Europe. At least generally in the UK drinks are served by the people working there and the machines are behind the counter.
I remember some years ago burger king sometimes had self serve drink machines. But cannot say I've been inside one in the UK for some time. So may no longer be the case.
The other exception is Costco which seems to work like an outstation of the USA over here. They have the self serve drink machine that is almost always out of syrup and allows refills.
Having said all that it does seem like penny pinching.
Not even penny pinching. Gouging. You could steal gallons in a cleverly disguised backpack and still not even negate their profit from the 3 bucks or so you paid for a cup.
Here in Finland, since their return in 2013, Burger King has sought to differentiate from other chains by having self serve drinks and unlimited refills.
Yeah, our BK has that s well. Love it because you can mix the different options. I always mix regular with Lemon Fanta (Fanta is drinkable in Europe :D)