The most popular article I've ever written on this blog is Save vs. Death Ray!. I love the fact that OD&D and the B/X line of Dungeons & Dragons had that saving throw category. But I've actually come to like Swords & Wizardry's single unified saving throw despite that.
What was important about saving throws in every TSR edition of D&D, and what's been copied along in most of the OSR games, is that characters improve their saving throws in absolute terms as they increase in level. A 9th level fighter is more likely to save versus any spell than a 1st level fighter. This is a significant factor in how TSR editions of Dungeons & Dragons made spellcasters less dominant. When the same spells were given in 3.x D&D, but with saves that get harder based on caster level, it made them more powerful. This was a serious design flaw, which helped contribute to casters being overpowered.
But the real reason I like S&W's saving throw is that it provides a good analog for the saving roll from Tunnels & Trolls. T&T had the unified saving throw 33 years before S&W did, although it was one based on the character's luck stat rather than their class and level, and it served as a handy roll for anything the referee or module designer felt was needed. While this isn't quite a universal mechanic, it's simple and flexible and good for many things other than dragon breath and death rays.
For instance, a saving throw with a Strength bonus may be used for when a PC is trying to hang on to a bar or ledge, while one with a Dexterity bonus could be used as a quick dodge roll. A particularly bad idea may call for a saving throw adjusted by Wisdom if the referee wants to be particularly kind. In more traditional D&D I've tried using the 5-category saving throws like this, but players get very antsy when you tell them to save versus dragon breath, and it loses the novelty after the second or third time. Other than dragon breath and death ray they don't generalize well and don't allow for enough interesting use cases, where a catch-all saving throw allows a blank canvas to invent uses.
Of course, some people and games like the Luck stat that T&T has, and I can't really blame them. But I think S&W's single save has more potential the longer I think about it.