Sperzel locking machineheads are well worth the money -even if only for massively speeding up string changes.
They do help with tuning a lot as there is much less slack string to deal with
They also help because they prevent issues caused by people not putting strings on right- as you just thread the string through, lock and tune.
They are about £55-60 a set unless you want gold ones.
But I agree that a well cut nut is essential too
See below - Graphtech have teamed up with tone-pros for a locking tunamatic bridge with graphite saddles.
Stability and tuning all in one - bonus

They said:
Graph Tech Guitar Labs and TonePros Sound Labs International have combined forces to create the SuperBridge, a TonePros® signature Tune-o-matic locking bridge featuring Graph Tech’s patented String Saver™ saddles.
Graph Tech’s String Saver saddles, made from a superior chemically-grafted polymer that includes Teflon, produce a 15% increase in sustain over standard steel saddles while virtually eliminating string breakage. The Tune-o-matic locking bridges designed by TonePros also improve sustain and acoustic coupling to the guitar while improving intonation. This is an unbeatable combination for players and manufacturers looking to improve guitar performance.