Hi to all on the forum,
I don't know if this is the proper section of the forum to post this, but here goes:

I am most familiar with a Schwinn Typhoon type of bicycle, coaster brakes, etc., and not so familiar with bicycle with derailleurs and hand brakes.

Why is the default setting (by this I mean the gear selectors are fully released and are applying the least amount of tension to the shift cables) of a bicycle set up so that the front derailleur is on the biggest sprocket and the rear derailleur on the smallest sprocket?

This means that the bike is in the highest gear, and if you want to go riding, you would most likely want to immediately shift into a lower gear.

Wouldn't it make more sense for the bike to be in its lowest gear when not being used? Then you could jump on and start riding right away, without having to immediately start fumbling with gears and all?

I don't understand your concern, since you need to actively shift the bike into a specific gear, it doesn't default to a gear. You would have to remember to shift down when you stop no matter how the derailleurs were configured.

But, to answer your question:

1) Actually, the front derailleur will shift to the small chainring if the cable is released.

2) The reason the derailleurs default to the smaller sprocket is because it requires more effort to force the chain onto a larger sprocket than it does to drop it to a smaller one. A small spring mounted in each derailleur provides sufficient force to drop the chain from large sprocket to small sprocket. A much larger spring would be required to go the other way, which would a) be heavier, and b) be harder to pull against when making your shifts the other way.

This is called high normal and most modern parallel derailleurs are set up this way although there are some low normal derailleurs that default to the lowest gear when there is no cable tension... modern ones are more complicated in their design.

Because of how derailleurs are designed and how they pivot and move it is simpler to build them with a high normal and simpler is better... the single sprung pivot design is efficient and elegant in it's simplicity.

My very old Peugeot touring bike has a derailleur that has no parallelogram but uses a coil spring and dual cables to move the pulleys and cage in and out and is a low normal as up shifting compresses the spring which defaults to low at no tension.

With this older design the low normal is natural and can be nice on a touring bike as a broken cable will not leave you stuck in high gear.

A few front derailleurs are also high normal and in the days of down tube shifters I thought this was the only sensible design as it put the left lever against and parallel to the down tube at speed and meant pushing it forward meant you were going faster...

When you park just set your bike in a gear yo can ride away on...

In the same vein as Sixy Fiver's comment, the low normal RD design is nice for bikes with bar-end shifters, since both levers get pushed in the same direction, i.e. pushing either lever down gives you a lower gear, and pushing up gives a higher gear.

The ideal set up with bar ends on a higher performance bike is to have two high normal derailleurs as this gets the shifters out of the way when you stand and hammer as you can sometimes hit them and cause an unplanned shift... on a touring bike you will sit and spin lower gears on climbs and when you stand up having a low and low set up gives you your lowest gear and points the levers down and out of the way.

Exactly right.

While the answers above are correct, they don't address the OP's concerns. The real answer is, "Don't worry about it."

OP - Just park your bike in an easy to start gear that works for you and don't worry about it, it will not damage the cable to be left for a while in the same tensioned position, so there is no need to make sure it's 'released' when you stop riding.

"For a while"? I have some bikes that I rarely ride, and I'm pretty sure I hardly ever leave them in their un-tensioned position (i.e., low front, high rear, presumably). Is this bad, or should I not worry about it?

Some people say it's bad for the springs to leave them "sprung", but I never worry about it

Default? There must be something wrong with your bike. All of mine politely stay in the last gear I was in when I rode up to the house and stopped. Then when I go out to ride away the next time they are still ready to go in the same gear.

Because the systems use a pull cable and a return spring they need to default to one direction or the other. Which way makes no difference at all.... or perhaps it does. A short lived movement called "Rapid Rise" occured when Shimano tried to reverse the direction of the rear derrailleur so that it pulled to the smaller cogs and spring returned to the larger. In practice there were problems so the system was only around for a couple of years. To see what the reasons were try a search here on BF for "rapid rise" or check it on google.

Actually it's still very much alive on many mountain rear derailleurs and is now called "low normal".

I think the OP's meaning by "default" is "when there is no tension on the shifter cables," i.e., the position the derailleur(s) naturally goes to when the cable breaks, for example. It's a good question in that it seeks to understand a concept of basic derailleur design. Hope everyone's responses helped clarify. Keep wondering and asking questions. Curiosity spurs one to learning. OP, it'd probably be good to work on enhancing your bike vocab.

Peripatetic, I guess I should have included a smily. I was trying to be funny.