I've seen several different implementations of this. There are a number of things to think about.
The basic issue is always getting enough break angle on the strings as they pass over the saddle. They have to press against it hard enough so that they don't hop off in some direction as they vibrate. One way to see this is to think of how you would make a very loud pluck by pushing the string down just in front of the bridge as hard as you could and letting it go. Obviously, if you push it down too hard it will come in contact with the frets so that sets a limit as to how far down it can go. As you play closer to the bridge the string will make more of an angle downward for a given displacement. The way the sting moves (which is not much like the way it's often visualized) it will make about that same angle upward a half cycle of vibration after you release it. if that upward angle exceeds the angle that the strings make downward over the top of the saddle it will hop off the top of the saddle, and the fixed point at the end of the string will be back at the tie block. At very least you'd get a sitar-like buzz.
Given that we can define the minimum break over angle. Note that the string doesn't have to break downward to be properly stopped, it just has to make some sort of angle in some direction. There is one steel string maker who fans the strings out sideways behind the bridge, and that works. On pianos they use a couple of little pins in a line and thread the string between them so that the length is defined. Most often, though, on fretted instruments we use a down angle.
For the string to bend downward something has to be pushing it up, and that's the bridge and top. To get enough down bearing each string puts a couple of pounds of down force on the top of the saddle. That sort of load on a guitar top will collapse it over the long run. Very early fiddles used flat tops, but they tended to collapse, so they started carving them to an arched shape to help resist that load. I have actually made a few arch top Classical guitars that worked out pretty well, but it's tricky to get everything into the right balance. The stiffness of the arch also changes the sound, of course, and you need to work out the best way to accommodate that.
On the usual tie bridge the down load of the strings on the top of the saddle is countered by an upward load on the tie block. The actual torque on the top is a function of how high the strings are of the top surface, while the break angle, which is a function of how far the tie block is behind the saddle, dictates the 'centroid' of the rotation: the point the bridge seems to rotate around. Normally there is also an upward force on the top due to the neck angle. At any rate, it's easy to make the top stiff enough to resist this torque over the long term without too much distortion, and without adding too much mass or stiffness that would impede the tone.
The main issue, as it turns out, is keeping the bridge from peeling up. Along with the torque there is a shear load on the glue line that is equal to the total tension on the strings. Because of the way those loads are taken in a glue line the maximum stress is along the back and front edges of the bridge. The torque, of course, pushes the front edge downward, reducing the stress there, but it pulls the back up, and that adds to the peeling stress along the back edge of the bridge.
It's fairly easy to take the shear load off the bridge. You just run the strings over the top of the saddle and down through the holes in the tie block, but then, instead of tying them there you tie them to a tailpiece that attaches back at the lower edge of the top. You get the same break angle at the saddle, and the same torque, but much less peeling stress on the glue line.
On Flamenco guitars they reduce the torque by making the saddle lower. Instead of the usual 11-12mm string height off the top they might use 7mm or so. This allows them to get away with a thinner top and lighter bracing. In theory you could have the strings simply emerge from the top at the correct point, or use a tiny saddle, and reduce the torque to practically nothing. The guitar might be hard to play unless you used a lot of 'over stand' on the neck and set it at a very high up angle, like a Humphrey only more so, and that increases the upward force on the top.
In the end, nothing about the guitar is ever as simple as you'd like it to be. The standard designs have been worked out to get decent compromises among all the competing requirements that work pretty well, but they are compromises. There's some wiggle room, but big changes can be difficult to make work right.