The last time I really remember feeling that sentiment was when the power was reintroduced back in "Up, Up, and Away." Busiek & Johns did a great job of making the power make sense, and the more I've thought about it since, the more I think that Superman needs to be super-intelligent.
I think about superheroes a lot, and something I find particularly fascinating is the concept of auxiliary superpowers: abilities that don't show up in the Who's Who or OHOTMU lists, but are necessary for the character's other powers to work.
So, for instance, anyone with super-strength must have some degree of invulnerability, because otherwise their tendons would tear and their bones would break every time they flexed. The Flash must be able to selectively alter friction and relativistic effects, or he'd catch fire and approach infinite mass every time he got moving fast enough1.
Superman's super-intelligence is a similar ability. Consider super-speed: the Flash can shift into a sort of "speed mode," where he perceives everything moving at a crawl. Superman, presumably, doesn't tap into the Speed Force, and we have no indication that he has that ability. In order to accomplish feats at speeds similar to those traveled at by the Flash, his brain would have to have super-fast processing ability. This gives him super-fast reaction time, and explains why he can do things like read and type at superhuman speeds. Without this aspect of super-intelligence, his super-speed would be useless at best and dangerous at worst.
I dislike the tendency to treat Superman's super-senses as things he can turn on and off, though I understand why especially early writers would treat them as such. You can't consciously decide to stop seeing the color red, for instance, or to stop hearing certain frequencies of sound, and I don't know why we'd expect Superman to have that ability either. But what we can do is focus our eyes on certain things in our field of vision, depending on distance, and we can sometimes tune out noises and sounds, especially constant, repetitive ones. So the No-Prize explanation is that Superman has learned to mostly tune out the sounds of insect wing-fluttering and the continental plates shifting, focusing his hearing on the sounds that are less constant.
In order to do this, his brain must have super-executive functions, able not just to process that information quickly, but to make sense of it, assigning degrees of importance and drawing Superman's attention to where it's needed. Part of that process is done by comparing sensory input to prior inputs--to memories.
The process of memory formation is complicated, messy, and dependent on the kinds of memories being formed, but part of the process of changing something from short-term to long-term memory is repeated passes through certain structures of the brain. There is a certain logic to thinking that this process would happen faster for Superman, given his brain's faster processing speed and increased need to sort through sensory input, but I'm no neurologist, and I'm getting into the area where I feel like I might just be pulling stuff out of my red shorts.
The case for Superman having perfect recall is shakier than any other part of his super-intelligence, but that also allows for a little flexibility in storytelling. It's easy to imagine that Superman can hold more things in his short-term/working memory--even if he couldn't necessarily hold more items in said memory at once (and I think he probably could, given the usual attention issues he already has to deal with), his processing power means he could be switching between items in his attention fast enough that it would seem like he was holding more items in his working memory. But as with humans, not everything necessarily makes the transition from short-term to long-term memory. So maybe he doesn't remember in issue #647 how to do a surgery he performed back in #328, but it's the same way you might have to look up the phone number for the pizza place every time you call.
From a narrative and theme perspective, I do think the idea that Superman has perfect recall of everything that happened anywhere around him on Krypton is pretty eye-rollingly silly. Remembering the minutiae of Krypton since infancy robs some of the tragedy of Krypton's destruction, and distances Superman from his human roots2. As much as I've come to embrace the Bronze Age, I'm still a firm proponent of the idea that Superman's powers should grow as he does, rather than having full-powered Superbaby on day one. His memories of Krypton, of his parents, should be fragmentary and fleeting, like any person's memories of early childhood. Krypton, for Superman, should be a place that he's studied, but not one that he remembers thoroughly.
Back to the main point, I think the trickiest part of "super-intelligence" is actually figuring out what that means--and that goes for the other smartest guys in the DCU too, like Batman and Lex Luthor and Brainiac 5. "Intelligence" isn't just one thing, but a combination of traits, and I think understanding what aspects of intelligence each of these super-intellects excels at is important. Superman's good at problem solving, with strong lateral thinking skills and an ability to make connections, in addition to having a keen journalistic and scientific mind and enhanced processing power. Batman's the world's greatest detective, brilliant at deduction, reading people, and predicting what's likely to happen in any given situation--usually by gaming out every possibility well ahead of time. Lex Luthor is a cunning manipulator, able to identify and exploit weaknesses in anyone, in addition to being one of the most brilliantly inventive minds on the planet. MacGyver can make a nuclear weapon out of some paperclips and rubber bands; Lex Luthor could turn the same materials into a time machine with enough parts left over for a jetpack. Giving Superman super-intelligence doesn't have to diminish these other characters, so long as we actually understand what that entails. In Coluan terms, Superman is probably somewhere around a 7th-9th-level intellect.
The issue of super-intelligence is an interesting one, but as far as I'm concerned, it's a necessary power, and a natural consequence of other powers we take for granted.
1. I realize that canonically, the Flashes have a "frictionless aura," but that wouldn't explain how they're able to get traction or grab things, or do those tricks with rubbing sand at super-speed to make glass. Hence, there must be a degree of selective control over this ability.
2. I also think it removes some of Supergirl's uniqueness. One aspect of her character that has only really been explored in recent years is that she grew up on Krypton, spent her formative years there, was immersed in Kryptonian culture and society. She's a teenage superhero "A Little Princess," orphaned and left to fend for herself in a strange land, without the comforts of home. She should be the one who remembers Krypton, not Superman.