IKEA Billy DIY bookcases without bolting in a wall. Is it a good idea/safe?
Screwing to the wall has nothing to do with capacity

Think about it. The furniture isn't necessarily directly against the wall, and a screw or very thin bracket reaching across some distance isn't going to carry much weight in shear. I.E. the wall doesn't ordinarily bear any weight.   

It's about safety

Ikea has a very strong message about standing furniture being screwed into the wall.  You didn't quite get the whole message.  It's to prevent furniture from toppling over and killing someone. Furniture topples over when its center of gravity goes outside its feet.  Examples of how that happens: 


It isn't level
the floor sags under the weight
someone grabbing the furniture to catch their balance or pull themselves onto their feet
Someone (e.g. child) trying to climb the furniture
All the drawers open
Heavy items in an open drawer not counterbalanced by heavy items in closed ones
Use in a mobile structure (boat, RV, #vanlife, "tiny house" on wheels)
Earthquakes
The top heavily loaded when the bottom is not (greatly amplifying the above)


Every piece of furniture from every manufacturer of the same size will have the exact same problem -- that is basic physics.  The only reason it's such an intense thing for Ikea is, they have chosen to invest heavily in their brand, which makes them targetable.  Likewise, people are sickened by Mexican food trucks and burrito shops every day - but it only makes the news when it's Chipotle.