We decided not to make what3words like this, even though this is different to most address systems.
One reason for not having this traditional structure of knowing what is nearby is to enable better validation and error correction. With other systems, for example latitude and longitude coordinates (or even post codes or zip codes), if you enter a pair of coordinates with a mistake (perhaps transposed two digits, or missed one out or mistyped etc.) then:
a) the device you enter those digits in will accept those coordinates as valid
b) the location represented by the mistaken coordinates is quite likely be in the right general area (unless you made a really bad error).
With what3words and a non-hierarchical system, if you make a mistake then the device you enter the words into will:
a) detect a word that is incorrect (a wrong word is wrong, whereas a wrong numeric or alphanumeric string can still look valid)
b) be able to suggest possible corrections (because there is a much smaller set of correct words)
c) be able to (help a human) eliminate most possible alternatives as all possible corrections will be spread a long way around the world.