It definitely helps to have it, fog, or no. As it works in most other situations where optical visibility ranges from limited to none. And unlike say AIS, it tells you what is actually out there & what isn't, including it's real world position, not where your plotter says it "supposedly" is. For example you can have buoys which either don't have AIS, or their AIS is DOA, & they've drifted out of place relative to their charted position. Radar will tell you this. Other electronic nav aids won't.
Radar can also be used to warn you when you're getting too close to something, or something's getting too close to you, by virtue of it's guard settings. So often it's an extra watch stander, one who rarely, if ever, takes a break. This is true even at
anchor, should you choose to use it then.
Or consider coming into waters with more restricted manueverability, or an anchorage after dark. Odds are Radar will give you the best real world pic of what's where. Well, other than perhaps a FLIR system costing as much as a new SUV. And the FLIR's range would be much more limited.
There have even been plenty of times when radar allowed me to easily thread my way through fields of crab pot floats after dark, & or, in thick fog. Not that I'd advise doing so in close quarters, but if you must, radar surely helps with it when not much else may.
And bottom line, any wise navigator wants as many ways to confirm his position, & those of other ships & nav aids, as he can get. Doubly, or trebly so after dark, or out past distances which are optically viewable.