The cross-draw almost disappeared not because it wasn't any good, but because of police concerns about someone grabbing the gun. This is easier with the cross-draw, and the cross-draw is a little harder to conceal then the strong side.
Strangely, the people who carry a Miami Vice type horizontal shoulder holster never think that they're putting the gun in an even better grab position.
However, it has some big advantages.
For one, your off hand can lift your coat or shirt out of the way as you draw the gun, and as soon as the gun clears, your off hand is right there to grab the gun in a two hand grip.
This is faster and less likely to foul the draw when you have to push the coat out of the way with the same hand you're trying to draw the gun with.
The draw can be a lot faster if your hands are naturally closer to the gun as when sitting or clasping your hands in front of you.
If you're sitting or have you hands clasped, your hands are virtually ON the gun.
This can allow you to have your hands very close to the gun without telegraphing that you're armed.
With a strong side carry you can't have your hands close to the gun without making it obvious.
In a potentially dangerous situation, with the cross-draw you can naturally clasp your hands in front of you and have your hand virtually ON the gun.
With a strong side, there's no way to get your hand close to the gun without making it obvious since that's a very unnatural position to have your hand.
You can draw the gun easily when seated, especially in a car.
The strong side may not be accessible at all if the gun is on the same side as the car door and since you're pressing close to the door, you can't easily get your arm back to get the gun.
As some police have found out, if you're sitting a little too close to the door with a strong side, and you slam the door, it can hit the gun and break a rib.
Cross draw, the gun is quickly accessible to either hand.
Strong side, especially in an IWB, you may not be able to reach the gun at all with the other hand.
One cross draw technique is to rotate your upper body away from the target as you draw the gun. As soon as the gun clears, it's pointing at the target. This also allows a close retention since the gun is being held away from any grab attempt, and close to your side.
If you also press the gun HAND, (not the gun) against your side just below the ribs, you can brace the gun for better control and make it even harder to grab.
Rotating the upper body also prevents sweeping the target.
While it's not really something that's that usable, one older gun expert taught to quickly rotate the upper body TOWARD the target, grab the gun, then rotate the body away from the target. This is sort of like doing the old "twist" dance.
This basically rotated the holster away from the gun as you pulled it the other way.
The down sides to the cross draw are a lack of lots of holsters to choose from, the gun is more easily grabbed, and it's harder to both position the gun for a fast draw AND conceal it well.
On the grabbing issue, Jeff Cooper wrote about a California narcotics detective who carried a .45 in the appendix carry position.
He always kept his hands clasped together in front of him in a hippie-like non threatening manner.
This covered the gun from grabs, and also had his hands close to the gun.
This also works well cross draw. I once knew a cop who simply kept his thumb hooked in his belt cowboy-style. This also covered the gun and left his hand ready to open his coat.
So, the cross-draw holster has a lot to offer if you can work around the weaknesses.