That's is impossible for two reasons: limited syllabes of mandarin chinese and linguistic union between dialects.
Mandarin has about 400 syllabes. When we add the tones to them we have about 1000 sounds. That's an extremely reduced set of syllabes that would make the adoption of an alphabetic system legaly unpractical: laws would be full of homophones, which would be the largest legal mess ever.
Besides, characters allow people of many other "dialects" (actually most of sino-tibetan languages) to understand each other without sharing the same language since they all are written the same. Do something against characters would be perceived by many chinese people as "going against national union". We cannot separate characters (in fact, the whole writing system) with their political menaing. In fact, as new dynasties reached the power, they usually changed the writing system as a sign of the "new order". As you can see, the writing system has always had an extremely high political meaning throughout chinese history.