Thanks for empirically testing this. The world is a better place when we test assumptions and gather evidence, even for “facts” as innocuous as this.
Pro tip: use a blender to make quick simple syrup you don’t need to wait to cool.
Simple Syrup is the first step towards peanut brittle. 
One of the easiest candies to make.
Sugar, water, and corn syrup cooked to a soft ball. Add peanuts, butter, salt and continue cooking to hard crack.
Stir in baking soda, vanilla and spread on parchment paper. Let it Cool. Break into pieces.
I used to make a batch every week for many years. I always gave away jars of brittle as gifts.
I’m at an age now that hard candy isn’t a good idea. I have several crowns.
Instead of brittle, I make peanut patties now.
Very similar recipe, except it includes milk. Cook it to a soft ball.
Done right, they are soft and won’t harm dental work.
Another reason to make a simple syrup by dissolving sugar in hot water is my: Old Fashioned Earl Grey. When making the simple syrup, I first steep a couple good Earl Grey tea bags in the hot water. Once chilled I essentially have a very sweet and very strong iced Earl Grey tea simple syrup. The rest of the recipe is per the traditional Old Fashioned cocktail.
Yes, I invented this version of the Old Fashioned and I won’t hear otherwise.
Not cocktail related, but when I was kid, pancakes for breakfast was accomplished by mixing maple-flavored extract into (hot) simple syrup.
ETA: not that that was the entire process, but it was a necessary step.
Another, oft-neglected, reason for making Simple Syrup: it’s easier than making Complicated Syrup. 
Oops. Sorry. I just lost track of time and my experiment. It’s a clear liquid now. Let’s see, what is it now on our clock vs my last post? Looks like 3 1/2 hours since my last post. So somewhere between 1 1/2 and 3 1/2 hours, without additional stirring, it completely dissolved. So looks like the ballpark 2-3 hours I guess is about right.
No, wait, there’s a tiny bit of undissolved crystals on the bottom. Just barely some. So maybe closer to 4 hours, or 2-3 hours if you stir it in regular intervals. Definitely not 45 minutes, though, at least not with my tap water (which, checking with a thermometer my tap was about 65F out of the faucet.) So, no boiling necessary, but a good bit of time required.
Maybe the mineral content of the water, or any other impurities, has an effect on the room-temperature time to dissolve sugar. Complicated syrup. 
Even with syrup, proper mixing isn’t guaranteed. When I put honey in my tea, I often find that the bottom fraction of an inch is sweeter than the rest of the cup was.
I made a batch today. 2 cups of sugar, 1 cup of water. Simmer for about 4 minutes with a few stirs.
I have noticed that the color varies a little. Occasionally clear, but mostly a somewhat straw color. I’m guessing that they don’t always get all the molasses out of the cane juice.
Or the sugar caramelized a bit while cooking.
Small hijack: As you stir in the baking soda and vanilla, add a tablespoon of red pepper flakes. AMAZING!
Possible I suppose, but I don’t simmer it more than a few minutes. I should check the temperature next time.
GaryM
No, you’re right. I’ve got my glass of finally completely dissolved 2:1 sugar:water simple syrup, not boiled, and it has the color of a chardonnay. Definitely not clear. Definitely yellowish.
I tend to buy gomme syrup for my mixed drinks: as much sugar as can be dissolved in water, with the addition of gum arabic to stabilise and prevent it recrystalising (and to add a slightly more unctuous richness).
Because when I want a drink that needs a little sweetening, I want it now, with a minimum of fuss. So there is a bottle of simple syrup in my house at all times. Ice, alcohol, other flavors if needed, squirt, done. The result with sugar is “similar” but not the same and takes more time to dissolve the sugar.
(Most people who use simple syrup make it in a batch, it keeps for a long time - ours is kept in a dollar store type plastic ketchup bottle)
In the summer, I usually have hummingbird nectar in the fridge (4 parts water, 1 part sugar), so I just use that. Not quite as sweet, but really, if it makes a hummingbird happy…
Except that, as I noted, the room temperature syrup solution I made yesterday also turned yellowish. As I said, it was about the color of chardonnay, maybe a hair lighter, but definitely looked like there was white wine in my glass.