Sausages are a staple of German street food, and yet most places serve sausages in a round "semmel" bun. But the sausages are long (duh) so they just beg for a longer bun. Why do you think hot-dog-style buns aren't more popular?
Wurst is traditionally not really a street food. Bratwurst is to be eaten on a plate with knife and fork acompanied by potatoes and veggies of some description. Preserved Wurst like smoked Mettwurst is dry and can be eaten without holding it in any kind of bun. Boiled wurst like Bockwurst or Wiener Würstchen are cooked in a soup or stew.
So traditionally there was no need to have a fitting bun for the Wurst. Bratwurst in a bun is a relatively new thing (post war I'd guess) and germans just made it work with the buns that were available anyway. People got used to that, so nobody saw a need for any different kind of bun.
That's my personal take, so take it with a grain of salt.
Your take on Wurst has no relevance for OP if by traditionally you mean 500 years ago. Who cares about 500 years ago? He wants to talk about recent events and you are here giving him a history lesson. 500 years ago NO MEAT was street food because most people were too poor to eat meat regularly. Of course you would treat eating meat like a special event.
Neither sausage-on-a-stick fast food nor sausage-in-a-bun fast food bear any resemblance to the traditional German way of serving wurst. Neither is "closer" they are both a million miles away from the original.