Why do they usually show old time sailing ships crowding sail?

I don't know where you got your information on the setting of sails on ships of the line, but they where so heavy that the often needed every bit of sail they could muster. If they where going into battle, speed was imperative. It's true enough that some of the faster boats would reduce sail in order to let slower ships keep up when the fleet was in route to it's destination.

Artist take artistic license with their paintings. Some Artist painted only ships at the dock, because that's all they ever saw. There is evidence that some artist never went to sea. So, they painted what they thought was what it would look like. I'm sure they looked at other paintings and something similar.

Well, yes it does look more dramatic to have everything up and flying, as Patrick O'Brien would say, 'Stunts'ls aloft and alow'...

and as sometimes happens, art immitates life...almost every sailing ship, merchant or naval, was bound somewhere...and the sooner you get there the sooner you can discharge your cargo, make money, turn around and come home, do the Kings business, resupply, get fresh water.....and a zillion other reasons. So by and large, unless it was a merchant ship with a penny pinching owner and rotted rigging and sails, every sailing ship carried as much sail as crew size and weather would permit.....

hardly any ship was driven like a China Tea Clipper or an American '49er, but, here's a secret: 9 out of 10 sailors want their ship/boat to make smart efficient passages and occasionally just sail to potential, running off 10 or 12 knots ( or 6 or 7 or whatever hull speed is) for hours on end and seeing the old girl fly

Well certainly a full rigged ship did look impressive with all sails set. Sails, however were there for a reason and no commanding officer would ever deliberately misuse his sails.

Masts very rarely broke as you say due to wind force, what would happen is that the sails would carry away first. A safety precaution in having the lighter sails uppermost on the Royals followed by the top gallants and gallants. The main sail was a sturdy sail and the lowest the coarse was as its name implies a very rough and strong sail.

The gallants, top gallants and Royals did not have reef points in them and in inclement weather would have to be taken in. The mains usually did, but not always. The coarse did and if after taking in your third reef on the course you would be left with the flying gib to try and maintain some control on the ship. At this time you would be in serriously bad weather.