The result is mostly the same as with your explanation, except yours doesn't explain why there are primary elections and how they can be so unpredictable.
Right, so the government should be based on brands rather than people. USA trying to make a people centric system still ended up into a brand centric republican vs democrat, just that now those brands changes dramatically every 4 years just people still vote for the brand even after it changes.
Its much more stable when you have stable political party brands like in multi party system, then a person voting for the same brand for 40 years will vote for roughly the same politics instead of it changing all the time.