I don't think that anyone is suggesting detailed fault finding techniques for digital electronics.
(which while not actually a massively difficult task with the right equipment, its very easy to find yourself twiddling knobs on several hundred grands worth of it in the process, which tends to put much of it beyond most folks DIY budgets)
At the simplest level, a hell of allot of kit can be saved just by spotting the caps that are bulging and spewing electrolyte all over the place. If you want to get a bit deeper, then you can do plenty with a multimeter, and even relatively specialist bits of kits like LCR component analysers or ESR meters are not that expensive.
(I don't agree that ukdiy falls down on diagnosis either particularly - we have some very good engineers here with plenty of experience in relevant fields. That does not mean that all contributions or all advice will be spot on, but its no reason to write it off either)
That works for many boards, but not all. In some cases a typical iron delicate enough for the size of task can't supply the heat on a multilayer board. That's where the hot air systems work well, either to temper an area of board to give the iron a chance, or more typically on their own just to reflow the obscured hole so it can be sucked clean.