Assassins should be encouraged to roam and play on surprise ganks (class rework idea)
Just being able to farm kills in mid lane isn't very assassin like. Assassins should come from out of nowhere, combo, and quickly escape with either getting a kill or severely damaging their target. They should not be a front line damage threat with no good way to combat them effectively head on unless you can out maneuver them or use items/skills that remove debuffs, adds invulnerability, spell shield, or stasis. Assassins should have to use surprise or higher mobility to kill their targets. No real assassin just walks up in full view and tries to kill their target after revealing that they are here to kill you. But that is what assassins in league do right now.
Start side note
, as the biggest offender imo, currently has no direct need to roam since most mid lane champions struggle to combat his combo effectively (most, not all mind you). His safe tower diving potential is huge and many items that combat his burst are receiving many nerfs. Items like 
and 
whose actives are necessary to give a chance to survive 's burst are having their usefulness gutted. has a longer CD and less offensive stats and 45 armor while also being the only defensive AP item with armor isn't very helpful. , well 
actually, is now useless for countering or 
. All that is left is 
and that isn't too helpful by itself.
Note that I am looking at these items as mid lane purchases, and not ADC, TOP, JG, or SUP purchases. Since they tend to not build these items first, second, or even third sometimes. Thus encouraging assassins to roam for easy kills, like assassins should need to do in general to be considered assassins. Assassins should have difficulty in a 1 v 1 when their target knows where they are.
End side note
Maybe add a mechanic to any champ who is primary labeled as an assassin, to receive a damage nerf to champions who have seen them for an extended period of time, and a damage buff for those who haven't. Similar to how 
deals increased damage to isolated targets, assassins should gain damage to unaware targets. Basically, to sum that up, if they are in FoW (fog of war), they gain a damage buff to champions. This buff also would last for a few seconds once exposed so they can still get a nice damage bursts to unaware targets. Firing spells while remaining in FoW which enemy champions see will reveal them and stop the buff. The buff would also need an activation timer so they can't just pop in and out of brush get the buff.