Assassin's being usable as good answers to priority targets is fine
Assassin's being the only worthwhile pick was not fine
Currently assassin's are a little weak, but not to such an extent that you can't pick and play them into and with the right compositions.
Look at pick rates mid for a second. Top 10 picks are Yasuo, Ahri, Zed, Lux, Annie, LB, Viktor, TF, Fizz and Diana 6 assassins, as well as an assassin like burst mage.
Top 10 jungles are Lee,_ Yi_, Xin, Vi, Elise, Rengar, Ekko, Shyv, Amumu and Eve. That's 8 champs with at least assassin like traits, all of the top 7 picks have some assassin like traits, meaning you can expect to be VS a burst based jungle almost every game.
Yasuo isn't a full fledged Assassin, he rarely 100-0's targets
Have you tried doing the maths on a 3 item Yas's burst? I assumed Tri/SS/IE and 18 for ease of calculation. He deals 2293 raw mixed damage +- around 50 based on runes and masteries. That's fairly up there with assassins like Akali.
Lee Sin can be built as a type of Assassin but requires snowballing to do so, and then to land his Q onto a priority target as glass in a team fight is significantly more difficult than other assassins.
Regardless of build Lee still plays as an assassin in 90% of situations, his burst and durability change but he's still basically an assassin unless he's playing peel.
Zed is an assassin, but is rarely played due to how 1-3-1 split pushing was hit and the strength of Dragon/Baron objectives now.
That's just factually incorrect. Zed's play rate is around 13%, he's the 3rd most popular mid after Yas and Ahri. (who I didn't include because she actually feels fair to play against)
Ekko can also be built as an assassin when solo laning, but has worse burst than other assassins if you avoid his R's damage, but is normally a jungle tank.
He's normally a jungle assassin, his most common build is straight AP. Him having bad burst is a myth, even completely ignoring his ult he has 1280+170% AP damage, assuming he never procs his W passive. Akali has 640 (not even making that up) + AA damage + 180% AP + 60% bonus AD in a single rotation.
Is Akali a low damage assassin? Because her numbers look about the same as Ekko's when you completely ignore two of his abilities.
Fizz is a bit ludicrous, but has trouble in the laning phase against many opponents and can struggle to get rolling as an AP Assassin. Changes to his ultimate along with ease of QSS/Zhonya's on carries helps keep him in check, but he's probably the best currently.
I don't think Fizz is that much of a problem right now. He's frustrating but he lacks the same BS factor that the other champs I listed have. He's also just a lot less popular.
Syndra actually can all-in assassin's just as easily as they can to her (except Fizz)
She gets pushed out of lane by all these champs, unlike them she has actual mana costs. Also her Q isn't even an ability until rank 3.
Zyra, Kogmaw, and Sona are extended team fighters, all-in assassin's are MEANT to destroy them.
I'd agree, but there should be an innate risk to doing so. When an assassin CCs you for 2.25 seconds, bursts you 100-0 in that time frame, then peace's out two screens away that just feels bullshit as hell.