"They" (the USN & USMC) eventually did. It was christened the F-4S. Some 200+ J-models were retrofitted to "S" standards.
F-4S was the designation applied to 265 (some sources say 248) F-4Js which were upgraded in the mid-1970s. This program was analogous to the Bee Line project in which Navy F-4Bs were upgraded to F-4N standards. The major goal of the upgrade was to prolong the life of the F-4J so that it could remain in service until replaced by the F/A-18 Hornet in Marine Corps service and by the F-14 Tomcat in Navy service.
Major changes included airframe and undercarriage strengthening. The aircraft were stripped and carefully inspected, and where necessary they received landing gear and wing/fuselage structural improvements. Visible external straps were added to the wing spar to improve the structural integrity. The electrical system was completely rewired, and the hydraulic system was replumbed using stainless steel tubing.
In order to improve the maneuverability, two-position wing leading-edge maneuvering slats were fitted to the F-4S, which gave a 50 percent improvement in combat turning capability in comparison with an unslatted F-4J. These slats operated automatically as a function of angle of attack, but they could be overridden from the cockpit. The slats came in two sections, one on the outboard part of the fixed inner wing and the other on the folding outer wing panel. Because of delays, these slats were not initially fitted to the first 43 F-4Ss, but they were later retrofitted.
The F-4S was fitted with the digital AWG-10B weapons control system with new AN/ARC-159 dual UHF radios and an ARN-118 TACAN (but not to all F-4Ss). The ALQ-126 or 126A deceptive electronic countermeasures set of the F-4J was retained, with the same short intake antennae fairings. One way that the F-4S could be externally distinguished from the earlier F-4N was by the shorter upper intake fairings of the S.
One of the persistent problems with the Phantom was that it tended to leave a rather prominent trail of sooty black smoke behind it, making it more readily visible to an enemy. In order to correct this problem, the F-4S was fitted with smokeless J79-GE-10B engines with low smoke combustors and low-energy ignition. This same engine was also fitted to some F-4Js.
SOURCE: http://www.f-4.nl/f4_27.html