I promise you that you will be hung if you have an accident/incident when using the "tower wind", as most ops manuals state, when the FMC shows something completely different !
For a good example read the Lufthansa Warsaw A320 accident report :
The crew did not turn to account the wind display on EFIS and did not consider the discrepancy between these data and the information on the wind given by air traffic services. They neither did take into account that tailwind component displayed on EFIS exceeds the value defined by OAM as acceptable for this aircraft