Gå means to walk. In a few contexts, it's used for general movement, but it's not used like English go. For example, saying "jag gick till Finland" implies you actually went there on foot.

Åka means to ride by vehicle, but probably not driving or propelling it. Furthermore, bikes are often not included in the verb, instead having their own verb cykla.

Pretty much for the same reason 'gone home' can't mean 'left his home'.
åkt hem as a combination means 'gone home'. If you want to say 'left (his) home', that's åkt hemifrån. Still a sentence like Han har redan åkt can mean 'He has already left'.

åka is only ever used for travelling in a vehicle.