The PAF sought the A-7 and F-5 in the early 1970s. One for the dedicated attack role (A-7) and the other for replacing the F-6 in the intercept role (F-5). By the mid-1970s, the U.S. approved both the A-7 and F-5 for sale to Pakistan.
However, the Carter administration wasn't happy with our nuclear program and was worried that we'd one day pair the A-7 with a nuclear warhead. So, the A-7 was shelved, but talks on the F-5 were actually proceeding. In fact, the PAF liked the F-5 because it was relatively low-cost and easily scalable -- for replacing the F-6, it was a good fit. To offset the loss of the A-7, the U.S. offered to sell the Maverick AGM with the F-5.
By the late 1970s, the PAF became aware of the shift to multirole aircraft, so it sent requests for the F-16, F-18L, and Mirage 2000. Only the French responded (with both the Mirage 2000 and an upgraded Mirage F-1). Carter softened up his approach a little by offering the F-16-79 and (according to WikiLeaks) loans for a potential Mirage 2000 purchase from France. However, Reagan decided to release the PW-equipped F-16s.
The rest is history, except... In the 1980s, the PAF was trying to decide how to build its future fleet. One option was to take the traditional "high-low" mix where it'd supplement the F-16 with a smaller multi-role fighter. For the latter, the PAF studied the Sabre II project, Mirage F-1, and potentially, the F-20. However, the PAF decided that this approach was not cost-effective, so it went with a different strategy: building around the F-16.
So, the new strategy was to build a large F-16 fleet: first with the 110 F-16A/Bs and (acc. to ACM Qureishi in an interview reflecting on Peace Gate) plans for 50-odd more F-16C/Ds. This would've been the workhorse fleet, but supplemented by various fighters in niche roles, like the Mirage III/5s and F-7Ps in the attack and air defence roles, respectively.
However, the inability to get the A-7 left a gap in a key area, one that the PAF hasn't solved to this day: the attack role. The A-7 was a well-optimized attack jet, and for the PAF, the ideal option for the attack roles it had envisioned. If not for funding constraints, I think the PAF would've gotten both the F-16 and the A-7 in the 1980s, but it could only pick one, and it went with the multi-role fighter (to rebuild the core).
IMO, if the F-16 program had gone as originally intended, i.e., 110 F-16A/Bs and 50 F-16C/Ds, the PAF would've sought a dedicated strike fighter to complete the vision it had with the A-7. Ironically, this might have been the scenario where the PAF would've acquired the JH-7A
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