See, just to name one, Tyrrell 003:

Last time a similar proposition was seen in F1 was in the Toleman TG183, 1983, by Rory Byrne.
Dallara fielded a prototype nosed in F3 in 1982, next year they went to traditional nosecone because the nose was hampering the flow to the venturis.
Yet these were exceptions; more or less the solution died some years before, when ground effect came.
Yet, apart from the obvious problems it gave on ground effect cars, it probably was a solution with some merits, since lots of people were using it.
It appears obvious it couldn't provide the same amount of front downforce as a winged design, and it was less adjustable so is it possible its strong point was drag reduction.
But how much? One would have expected to see these noses everywhere at Indy, if it was the case, yet it was seldom used there.
Was it possibly just fashion? Any data or recollections?