Sorry, this is not true. VFR aircraft have a LOT of leeway in airspace that isn't Class A (above 18,000), Class B (around huge airports), Class C (around less huge airports) or Class D (around other towered fields). You don't ever have to talk to ATC if you are flying VFR and stay out of that airspace. You can request specific routes on an IFR (an instrument) flight - in many cases they'll be approved, sometimes not - but many flights are not IFR.
There are airways - which doesn't involve specifying the type of aircraft that can fly on them. However, if you are flying in VMC (decent weather), and you aren't in class A airspace, there could be a VFR flight anywhere around you. There is more control in Class D, Class C or Class B airspace as all of the aircraft are talking to ATC but that doesn't cover any significant portion of airspace.
For example, on Sunday I took off from my home airport, did some maneuvering, flew about 20 miles into the next state, landed at a different airport, took off, flew over a separate airport and did a practice instrument approach back to my home airport. Not once did I talk to ATC, I communicated only on unicom frequencies to announce my intentions to the aircraft at the airports where I was operating (whether anyone else was listening or heard, I don't know). The responsibility was on me as a pilot to keep my eyes open and look for other aircraft. So let's say a drone is flying on its predetermined flight path through airspace shared with VFR flights. There I am, doing maneuvers, changing altitudes, etc. Am I really going to see something with a 2ft wingspan coming at me from the side? It's hard enough spotting another general aviation aircraft with a 30ft wingspan.