What's the downside of false hope?
Putting the rescuers in danger.
Every rescue worker going in is putting his life in danger. to a certain degree. They needed to stop work because the structure is unstable.
They have not pulled anyone alive since the first day. There has not been any sign of life in almost a week. Even if someone ended up in a void without getting crushed on the way they would have had to contend with fire smoke and dust, and a lack of food and water.
A false or highly implausible sense of hope will drive rescuers to take unwarranted risks with potentially deadly results.