Bikes at Walmart have suspension. Cost isn't the only factor. Now, Walmart suspension may not be the best for a 500 pound load. One could build a bike with a double rear MTB spring to get fairly good spring for heavy capacity. Perhaps a bit different design on front if one is using off the shelf parts. But, it would be easy enough to spring the head tube independent from the rest of the bike. Hmmm, it looks like Riese & Müller is springing the fork. Which then means a pretty custom fork if done right. Anyway, I doubt cost is the only factor.
As far as safety. I don't know. I've never felt bumps made me unsafe.
Ahhh... you're in Germany. I'm in the USA. Things may be different. Do you have cobbles? They're rarely used here. So, most of the riding would be on pavement. Yeah, they'll be bumps, but nothing that one shouldn't be able to handle.
The only advantage that I can really think of is that it might protect the bike slightly. Say you're running along and hit a 2x4. Without suspension, the front of the whole bike, then the rear will have to be lifted, travel over the 2x4, then return back to the previous position. That sudden jar may be hard on a bike with a heavy load. On the other hand, hit the 2x4 with suspension, and much of the difference will be taken up by the suspension, and the load more or less maintains the former place/momentum.
Anyway, a quad would more or less require full suspension so the wheels can stay on the ground when going over bumps.
A trike would be less prone to one wheel bouncing off the road and losing traction.
A bike even less so.