The potential problem with bright midday sun on a clear day is hard shadows cast by the direction of the light hitting three dimensional subjects and scenes. Bright directional light can result in very hard shadows cast onto important parts of your subjects/scenes that in many cases isn't that flattering. Not all subjects will cast these shadows and the direction of the light vs the subject can make these images work out ok. For instance shooting a photo of a two dimensional main subject like a flat billboard in hard directional light is often just fine as it doesn't cast hard shadows onto itself. And depending on the direction of the light and the pose and shape of the subject it can sometimes work with live subjects but often doesn't work that well.
This isn't really limited to daylight, flash photography with one bright directional flash can lead to these same hard shadows. But in portrait and some product photography that directional light is sometimes used to great creative effect and the same can be done with some thought and luck on the photographer's part outside on a bright day. IOW, it's certainly possible to use hard directional light well and some scenes/subjects lend themselves to it more than others and like all creative things there are no hard and fast rules or at least rules can be broken to great creative effect on occasion.
When there's passing clouds or high thin overcast it's a lot like a giant soft box in the sky diffusing the light so it's less directional and hits our subjects and scenes at a broader range of angles filling in a lot of the shadow areas and minimizing dark blocked up shadows. Personally I like thinner clouds so that there's still a directional nature to the light most of the time. IOW, I prefer to still see some shadows cast by objects like trees but with some lighter overcast or thinner clouds so that those shadows aren't as hard and dark. Sure, complete overcast where no shadows are cast can be used as well and sometimes can result in great images just like bright direct sunlight can sometimes be used for great images but in general a bit of diffusion that retains shadows but softens them is what I often look for. Retaining some softer shadows can help give images a more three dimensional look and bring out things like fur and feather detail that can be lost in completely overcast conditions.
When I shot weddings, many were outdoors and typically in the middle of bright sunny days. It's something wedding and event photographers have to deal with all the time. Sometimes a bit of fill flash or even full studio lighting (e.g. soft boxes) can be used to modify harsh light but often for more candid shots and ceremony shots I had to make do with available light and work towards the best shots under the circumstances. A bright white wedding dress right next to a black tuxedo in harsh midday light is a real dynamic range challenge but one nearly every wedding photographer sees all the time. If you can't use additional light (flash, bounce card, light reflecting off of buildings, etc.) or can't shoot in the shade then you just have to deal with it and many memorable wedding photos have been captured in those less than ideal lighting situations.
As wildlife photographers I suspect we've all come across interesting subjects in harsh light and sometimes we'll just shrug and continue to capture photos and other times we'll look at the scene, the light, the shadows and just pass. The more common the subject and the less unique the behavior the more likely I'll just pass on a wildlife subject in the middle of a bright blue sky day but sometimes we still capture those photos and sometimes they surprise us and work out just fine either due to just how the light was hitting the subject or due to some harsh lighting creative effect.
To me the bottom line is that harsh midday directional light casts hard shadows that are often problematic and softer diffused light either near the edges of day (diffused through the additional atmosphere the light passes through when the sun is still low and near the horizon) or with some clouds to break up and diffuse the light or when shooting into shadow areas without the hard directional lighting is preferable. Also from a wildlife perspective, a lot of the wildlife subjects I shoot are more active near the edges of day and often more active on cooler cloudy and overcast days which is another reason I prefer shooting under those conditions.
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