The nut will typically stabilize it enough for most purposes. The real issue becomes if you take the legs off the machine to move it, you need to lift the playfield (if in back) to get a wrench on the nut. But, if you do not plan on moving it much, the nut/bolt approach should work. I also note that there are some difference in the leg mounting bracket depending on era and brand of machines. The ones Mick showed should work for any recent Williams/Bally/Stern game, but would not for some older solid state games.
Ron