You must be fairly new to boating. There was an age, not so long ago, when EVERYONE operated without radar, always. Relatively recently (say the last 30 years or so) small radar sets have become practical to fit to small yachts. Even more recently (the last 5 years or so) they have become practical to run on small (ish) sailboats. And yet, in that time, collisions in fog were not markedly more frequent between small boats than they are now. Part of this may be that now, everyone thinks running around at high speed in the fog is perfectly safe - I've got radar, after all!
I already said upthread, and I'll say it again for emphasis, radar sets are now cheap, get one. But the whole idea that without it we should all stay off the water is ludicrous. Safety in fog is 95% up to the loose nut behind the wheel, and 5% electronic assistance.