If I had to guess it's because of its exotic look. Ventral intakes were almost unheard of back then.
Exotic/modern is one aspect of this, but the P.1121 was simply sleek and clean too. Looks matter a great deal in an unbuilt design gaining a "cult following", futuristic and/or brutish can work just as well as elegance, but it better not be downright ugly (F-32, looking at you!).
The main problems that I don't see being addressed are: it's too big/expensive to compete with F-104 or Mirage on the export market, and it's not as capable as the Phantom which set the gold-standard for it's contemporaries among those countries who could afford it.
Well, thinking outside the box a bit, there is a precedent. In terms of size, the MiG-23/27 is roughly similar, and that family sold well into the quadruple digits! This would seem to indicate that fundamentally an airframe adaptable to both A/A and A/G roles, sized in the bracket between the Mirage III and F-4, is a militarily useful thing. A market niche should therefore exist, though of course the P.1121 could not compete for the same customers (except, notably and repeatedly, in India!). Perhaps as with the Flogger this would take the shape of distinct A/A and A/G versions rather than having both capabilities in the same airframe, so a Jaguar-style chisel-nose variant?
Maybe some of the sales which the F-4 or Mirage III gained only came to pass because there was nothing in between available? It's an assumption that they were optimally sized in every case.