Why the leading edge devices?
A definitive answer requires input from someone in the project office at the time, but a few pointers are clear: the Trident was designed to be as fast as was feasible in the early 60s. This meant a good high speed wing section, and with the wing sections available at the time, a relatively high sweep back (I don't recall the exact number but a comparison with the 1-11 shows that the Trident had a lot more). Such sections are also not noted for good high lift at low speeds so a degree of 'variable geometry', in this case camber, was needed to keep take-off and landing speeds, as well of course field lengths, within bounds. As it was the aircraft had the reputation of a ground gripper (though that has a lot to do with the installed thrust). Its contemporary the 727 sprouted even more impressive high lift devices as Boeing wanted even better field performance though I think they weren't aiming at quite such high cruise Mach (T1 MMO - M0.88, 727 0.84 at a guess). Nowadays advanced sections allow the same Mach cruise with about 15 degrees less sweep and better low speed performance, but once the moving leading edge genie was out of the bottle it was employed to optimise the designs and all the current crop of airliners use them.