You can’t just use any IP: some are truly special (e.g. the multicast range) and 240/4 is still treated as invalid by many currently deployed IP stacks in their off-the-shelf configuration. Getting away with this only works at the kind of integration scale where you’re smelting your own copper, so to speak.
The actual probes are tiny consumer grade routers (https://www.google.com/search?q=ripe+atlas+probe&tbm=isch) with a new firmware. RIPE provides these free of charge to volunteers (people and companies) who then run them in their network (e.g. homes and datacenters). (Of course larger form factors are available to volunteers with more in-demand locations.)
In return, volunteers get rewarded for uptime of their probes with credits that can be used to request custom measurements from the Atlas network.
There are probes _everywhere_; not just in terms of geography (https://atlas.ripe.net/results/maps/) but also in network locations that you cannot get access to via any other means; there really is no other service that comes close in terms of reach for global internet status testing.