Because "bramka" means literally: "a little gate", so you may translate this word as "a goal", "a tagret" etc. "Siatka" means literally: "a net", but a player cannot run to a net, it sounds weird in Polish. You can say: "Piłka wpadła do siatki" - "A ball fell into a net", but it sounds weird in English, on the other hand. I think this translation above is correct.
It's relatively rare and generally sounds a bit old-fashioned. However, there are certain fixed expressions where ku is absolutely fine. There are also certain verbs which work well with this preposition, like zmierzać and skłaniać się.
According to the corpus the verb biec and the preposition ku also commonly appear in pairs and in the extended corpus I could even find several examples for biec ku bramce.
Added: 'ku bramce'.