The problem is frontal area is higher, so more drag. Wetted area[1] is also much higher, so there's a lot of skin friction.
The advantages are (theoretically) lower structure mass per passenger. But airplane cabins are pressurized, and lightweight pressure vessels 'want' to be cylinders or spheres, not big flat boxes.
There's a aerospace engineering student who gave a thesis talk on the disadvantages of blended wing-body, and offers some possible solutions.[2]
[1] https://en.wikipedia.org/wiki/Wetted_area
[2] https://www.youtube.com/watch?v=IWBaddGG6z8