Most sustain damage is bullshit, as its having the most CC and having the most waveclear.
However it is true that their mobility is generally the highest, and many "new gen" assassins have very low cooldowns on their main damage as well
so their sustained output is not bad or even pretty good even if it is not the highest.
Highest DPS however is a title that exclusively belongs to master yi and the marksmen alternatively depending on balance, kayle might have had a foot in there but i think some nerfs saw her drop out of it.
The assassins waveclear is also set so that it´s better than most early although mages will almost always outscale them in this regard, some mages do not but they usually have other perks.
...
Yikes though, i myself absolutely despise assassins but it the boards have truly been flooded by complaints against them recently....is this another reddit invasion or what? O_O