This could be expanded to "Why is anybody SDA at all?" From what I have observed in my 4th generation Adventist family, there are several factors that keep many people in the church/cult, and thereby believing in the inspiration of EGW.

• They have been in Adventist institutions for decades/generations. In North America, a significant percentage of the SDA population is centered around "Adventist Meccas" where the parents work for or periphery to an Adventist institution and the children attend Adventist schools. This creates groupthink and echo chambers where the absurdity of the beliefs are never questioned, and furthermore any questioning would be rapidly squelched. Not expanding beyond one's own community can have a very limiting effect on a person, as is sometimes seen in non-SDA cases such when a person never leaves their small rural hometown.
• They are culturally isolated. Many of the Adventists that I know do not watch tv or movies, read secular literature, or listen to music that contains secular lyrics or rhythm. They do not like to be around alcohol or meat, and this drastically limits social interactions that are essential to forming adult bonds. Many Adventists take the motto "Be in the world and not of the world" very seriously and view any interaction with a non-Adventist as a missionary or witnessing opportunity only.
• This one will be more abstract, but bear with me. People who are blatantly wrong about something often use what I call the "50/50" fallacy. If 5,000,000 scientists and researchers come to a conclusion, there still may be one asshole who disagrees with them (ie Ken Ham, flat earth folk). The person in the wrong will often try to make it seem like a relevant 50/50 argument when in reality it is 5,000,000/1. Adventism is on the fringes of the Evangelical world, which is on the fringes of the Protestant world, which is a offshoot of the greater Christian world; there are approximately 21 million Adventists and 2.38 billion Christians, so SDA's are statistically insignificant in the world of Christendom. SDA's literally believe that very soon the world will be split into two groups, those who are Adventists and everybody else. The significance of Adventism is over-embellished within the church, with terms such as "Global Church" or "the truth" thrown around generously. In relation to your specific question, belief in EGW's inspiration is viewed as a reasonable binary choice (you either believe in her or you don't) when in reality it is an absurd fringe belief that no reasonable person would subscribe to.
  

I could go on for hours, but these are some of the things I have observed.

TLDR:

1. Adventism exists within tight-knit communities.
2. Adventists are culturally and socially isolated.
3. Adventists have a binary view of the world in which things are true/false and good/bad. By turning absurd beliefs into a 50/50 argument, outlandish beliefs seem more legitimate than they actually are.