Mechanisms are easy to make, are useful and are quite valuable.
Using 50 rocks and a mechanic, you can put 25 traps around your fortress.
Using 20 rocks and a mechanic, you can generate enough wealth to buy a lot of stuff from a caravan with wagons, though a craftsdwarf will do this better.
You can do all of this as soon as you start digging.
But have you ever seen a mechanism made of rock? Well, a small enough mechanism that a single dwarf can carry? Maybe the dwarves are that good at carving rock that they can make small gears and axles out of it, but metal mechanisms make more sense. Take a look:
1. They make troops much more viable. Now that you can't build dozens of traps without a robust metalworking industry, you need your troops to protect the fortress.
2. Mechanisms become worth their high value. If you decide to export some, this means you are exporting your hard-mined metal (or hard-killed goblins).
Different metals could affect the quality of the traps, for example. A weapon trap built around a steel mechanism would jam less often than the one built using a copper one (it should depend on the quality of the mechanism as well, of course). When proper sieges are implemented, a gabbro door kept closed by a pewter mechanism would not be very useful.
If even more advanced water pressure is implemented, very sturdy mechanisms will be required to open and close the floodgates that dam, say, a major river or a huge reservoir.
Some environments, especially those that lack either fuel/magma or ores, will become even more challenging, as the dwarves will depend on either the starting stocks or the caravan supplies to make all sorts of mechanical contraptions.
tldr: Metal mechanisms are good for the game.