Quality of skills on an amulet worth?

Probably not a useful as caster. Minion builds see the most benefit since most minion gem quality increases reservation efficiency

Falling Thunder has a line "20% more damage per power charge consumed" at 20 quality and at 25 it would go to 25%. So at 7 power charges I'd go from 140% more to 175% more damage, which is just flat out 25% more damage dealt from that quality roll alone.

Flicker gains crit chance per quality, which can potentially free up some passives or suffixes on gear,

I would definitely use this on my monk, the 5% quality roll is better than T1 crit multi for my setup specifically. The prefixes are perfect as well since many monks choose to go CI.

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Don’t listen to the people who will tell you this isn’t a good stat - it’s a great affix. It can make huge differences with certain skills. Especially given that we’re in a league that allows for 23% quality skill gems and also 5% quality socketables that using just one in gear brings 23% quality skills to 25%.

People have already pointed out Falling Thunder as a skill that benefits major from quality - another one is Lunar Blessing. Quality massively increases the damage as cold buff that it gives the player. This type of thing goes for a lot of skills.

In addition we have skills that we can’t innately apply quality to so it has to come from gear and supports - such as Shred (quality gives a good attack-speed boost) or any skill that comes from a weapon or ascendancy.

Not much melee skills that will profit from gem quality.