Probably the age...
Actually, the issue is not what will it be fighting as much as how long can you really keep the Harrier flying? The minute you let a weapon system get ground into the dirt (as they're having to do with the early model F-15s) and don't have it's replacement, you're going to have problems, especially because your enemies KNOW that you're stretching the life of your aircraft and they'll then exploit that (maybe they won't attack you directly, but they'll exploit the weakness elsewhere that you would normally intervene). It happened once before - Korea. Korea in part occured because at the time the "Allied" powers under the guise of the embryonic United Nations had aircraft and equipment that was rapidly running out of useful life, contracts for replacements cancelled wholesale, parts contracts cancelled, thousands of viable aircraft (and spare parts) being scrapped every month, sometimes in place, the atmosphere was ripe for North Korea to attack and they did. For a bit, they got away with it too.
So, let's come to today. There are 2-bit idiots (dictators) around the world looking for the chance to do nasty things. However, there's one problem - the US and it's Allies (and sometimes the UN). They have a military that can stop them from doing those things. What if they were crippled because one of their mainstays was grounded permenantly (like the F-15 or Harrier) and there was no replacement in sight?
Also, remember that just because we don't have a "big, bad Soviet Union" to fight now, that doesn't mean that development of advanced aircraft and weapon systems has stopped. The Chinese (still very much a threat) and Russians continue to develop advanced fighters and anti-air systems more than capable of wiping every Harrier off the face of the earth in very short order. Not only that, but they are selling those weapons to countries that are definitely not friendly us (the US, UK, and Europe), like Iran. We may not be facing the overwhelming numbers that we did before, but that doesn't make the need to have the aircraft any less, just the number we need to complete the mission smaller (250 F-35Bs for the RAF & RN vice however many Harriers were in service at the peak of the Cold War).
Anyway, to tie this into the original thread - the US crippled it's Tactical Electronic Warfare capabilty when it retired the EF-111 without a replacement and asked the small EA-6B fleet to do all the EW tasks for the US Military. They've managed to do it, but in the process have severely strained the airframes and their life is running out. They have a replacement in the wings, the EA-18G "Growler", but it will be deployed in even fewer numbers than the EA-6Bs, so they will have to do the same amount of work with less aircraft. It's a sad situation all-round.