Which has nothing to do with the development of a new EMH. As revealed in Voyager as well the EMH Mk. 1 was ridiculed heavily to the point that Zimmerman wanted to distance himself from it.You go watch Voyager especially one of the last seasons when theyre close to getting back home. They figure out a way through holo communication or whatever. Zimmerman even tells Doctor that hes dying from some wacky Star Trek disease.
More on topic, Bashir makes an ideal target. He can gain access due to medical clearance, meet with people privately, and generally has the infirmary to himself. Being Worf or Sisko engenders too much risk, while lower lever allows less scrutiny.