Flash allows you to take a passable photo anywhere. And as such, if you have to take photos on demand with little control over location (like Runnah's construction photography for instance), then a flash is not only useful, but pretty much mandatory on a sunny day, because it's the only way to make the photos not horribly harsh.
However, in my opinion, flash as typically used for outdoor shots looks a little forced to me, and unnatural, and I don't prefer it (i'm talking quick handheld type things, not huge studio outdoor setups with assistants and multiple lights etc. which can look just fine).
In order of aesthetics, IMO:
[sunny day, subject in sun, no flash] <<<< [sunny day, subject in sun, flash used well] << [sunny day, subject placed strategically, no flash] << [fully controlled lighting like a portrait studio OR outdoors if you're mostly overpowering the sun anyway -- though squinting is still an issue]
But "strategic placing" is very difficult, and there may not be more than a handful of convenient and suitable locations in an entire small town for taking good photos at the hardest times of day, like high noon in the summer. An example of such a location AT high noon in the summer would be:
* a fairly narrow, but-not-too-narrow east-west alleyway
* with an interesting looking southern wall
* and a uniformly light colored northern wall and ideally a dark (like brick) southern wall
* where the southern building is no more than about 2-3 stories tall, and
* ideally long enough of an alley that you can position the subject far enough away from the far end of the southern wall to blur it out if you so choose.
This would allow you to place the subject in open shade so no direct light or harsh shadows, BUT the sun still hits the northern wall, and reflects right back immediately onto your subject, giving you a directional, city block-sized softbox. Shoot the model with the dark wall as background for manageable dynamic range, and turn them a bit to one side or the other to get butterfly or loop or rembrandt etc. key lighting. Then use a reflector to fill in remaining ratios as desired (works better for more control over this if the south wall is dark and thus not already reflecting too much)
If you can swing something like that, I think it tends to look much better than flash-fixed lighting. Which is great, but there might only be two places like that in town on public property... and you have to have the freedom to go there, which you won't if the shoot has a fixed theme or needs to be done on a specified location.
Gazebos are also nice in that they allow controlled shade at any time of day, and are usually in parks that serve as nice backgrounds. But the reflected main lighting is less directional and controllable and less uniformly colored than in the alleyway example (coming from skyshine above AND grass below AND trees to the side, etc. all about equally)
tl;dr: If you have the freedom to make the stars align and line up a highly controlled, strategic natural light only shot in midday, then it will look the most natural. If you have ANY constraints on your time or location, though, a flash is a lifesaving necessity in midday.