I honestly think you have this backwards.
There's more than one dialect of English. There's no requirement that they're consistent. Indeed, there's a famous story about a misunderstanding due to speakers of different dialects of English agreeing to "table" an item during a meeting.
Reaching a goal can become squishy, because sometimes we reach physical goals, like Oshkosh, and sometimes we reach for abstract goals, like a new high score at Sudoku on my iPad. If I can still be here while I reach the goal, I suspect I can use {SIch}, but if the goal requires the whole of me to be within the named area, I think I need to use {paw}.
To "reach a goal" is an idiom based on a metaphor: treating a desired accomplishment as if it were a physical place. If you're climbing Mt. Everest, you can {paw} at the summit. If you're learning to slam dunk a basketball, you can {SIch} the rim. If you've made a new high score at Sudoku on your iPad, I'm sure that's neither {paw} nor {SIch}, but {chav}. In English, these can all be expressed using the verb "reach". In Klingon, they are considered distinct ideas.
The difference between these two verbs is that one involves moving the whole of you to the goal {paw}, while the other involves extending part of you to touch the goal {SIch}.