Keep in mind that the protocol is a bit rubbery -
(a) the steady wind is presumed to reduce within the notional boundary layer so it probably will drop off approaching the runway - the half factor attempts to handle this in some sort of rational way
(b) the gust is presumed to be random so it might catch you out at any stage of the approach - better to allow for all of it through to the landing
(c) 20kt max tries to balance having too much against too little IAS approaching the runway
Nothing at all terribly scientific in this stuff - just an attempt to load the dice in the pilot's favour.
A few other threads on the subject have more description on the considerations for those interested in running a search.