SMOE, during Vietnam, F4's doing CAP often would carry the "pistol", a centerline gun pod. With no modern avionics or site, it was a crapshoot. Once the F4E came along, using the gun became much easier from what I've read. I read an article written by Ritchie, the first ace in the F4 for the Air Force, and he talked about forgetting about the gun in the F4E during one fight, he was so used to not having one, or a reliable accurate one, in the older models.
The OP question I think is odd. The USAF, US Navy, and USMC all used the F4, everyone knows that, but they also had other types, types that matched up very well to the Mirages and Kfir's. The Navy had the F8 Crusader in that time period, an excellent single seat single engine fighter, very maneuverable, great thrust/weight for the time, and 4 decent reliable guns. Sounds like the perfect Israeli fighter to be honest. There was also the A4, again, used by the Israeli's, plus smaller lighter "Mirage" types that the USAF had like the F5 and others.
I think Israel just made the best of what they had, or better said what they could get during the time period specified. Also, the OP being from Israel, I'm sure he knows better than us, but the airspace isn't all that big, and you don't need as large of a fuel carrying monster like the F4 in order to do the job. Also regarding the missiles, Israel was smart enough to figure out that the missiles of the day weren't reliable in the least, even the best Aim9's at the time had laughable firing parameters, and even then 2/3's of them missed or didn't work. So, they focused on the gun. Nearly every video you see of the IAF during the wars of 67 and 73 goes on and on about their a2a gun kills. I'm pretty sure the reason is that the IAF trained their pilots to use the gun to great affect as the missiles on both sides, US and Soviet, just weren't all that lethal yet. The enemies of the IAF probably didn't focus on gun training as much, if at all, and didn't know how to respond to close maneuvering Mirage, A4's, and even F4's of the IAF. Just what I've read, but it seems pretty valid.
So, IMO, the reason the IAF used the F4 primarily as a strike fighter was that during that time the IAF identified that a: they didn't need such a longer range fighter in their close range airspace, b: the missiles were terrible, and to focus on using gun armed fighters, which the F4 wasn't until the E model, in the early 70's, and even later for the IAF, c: The Israeli defense establishment could far more easily copy Mirage fighters and manufacture them than they could F4's. This all said, I realize that the IAF did score a large number of kills with missiles during the wars of the period, but god only knows how many missiles missed or just didn't work, I'm sure it was along the lines of the US in Vietnam, which was a lot. Having the skill and capability to gun enemy fighters probably made a big difference in IAF survival and kill ratios.
The last point, c:, I brought up regarding Israel making its own fighters like the OP alluded to is important. They never "made" their own during that period, is was much more of a reverse engineer and re manufacture type of deal I believe. The F4 was far larger and more complex than the Mirages, and the parts were probably easier to either source through grey area means or to build in country for Israel. That and the fact that the F4 wasn't the optimal aircraft for a cheap a2a fighter with a ground attack capability anyway. Israel did eventually get there IMO. The Lavi was a nice little fighter. It's called the "J10" now in China. Of course Israel protests that it would never, EVER betray the US and transfer weapons tech to China like that (snicker, cough), but all sources say that it not only looks almost identical, that China actually received a flyable Lavi once upon a time.