You're overexaggerating. I main at 4 assassins and 2 divers. I never had an issue with shields (except for early Barriers in the midlane, fuck those).
Assassins are not supposed to burn through 6k HP.
Assassins are meant to infiltrate, kill QUICKLY and get out. All they need is a chance to catch the target undefended- that is, preferrably, WITHOUT 6k worth of shields on top of them.
How do you do that?
##Disruption.
Your team needs to provide you a window to strike.
I play Katarina, Kha'Zix, Ekko and Talon so I know what each of them needs to function.
- All that Katarina needs is an AoE CC on grouped enemies. Pick an Orianna or Amumu for her and she'll ace the enemies on her own. She HATES isolated enemies so you need big CC to hit everyone at once.
- All that Kha'Zix needs is enemy separation. Janna, Camille, Gragas, Tristana, Zac. Give him a moment alone with a squishy that's a bit too far from their team and they're toast. He hates grouped up enemy teams, so separate them for 2 seconds and watch him go ham.
- All that Talon needs is the target to NOT get healed or shielded for 1 second. Pretty much any tank can provide enough disruption for that. Isolation, peeling, mobility, he doesn't give half a shit about all that - as long as the target can be burst down, he cannot be stopped.
- All that Ekko needs is a good, heavy frontline that can keep the enemies busy for long periods of time. Ekko, in contrast to other assassins, needs time to get going. So you don't want burst CC like Malphite, but instead, you want less powerful but CONSTANT disruption so you can weave in and out of combat. Many tanks and control mages do that, like Anivia, Nautilus, Sejuani etc.
Of course, all the other assassins have their own methods and needs, my expertise is just limited to these 4.
Each one has their own strengths and weaknesses. All will get the job done, however slightly differently. And they need different things from their team.
However, trust me. Early game, mid game or late game, assassins CAN and WILL kill the target if you're good at your job and your team is decent at theirs. I know these well-defended carries are hard to kill, even for assassins, but really, trust me. That's what they're designed for.
Of course, if you pick Katarina into a team with no AoE disruption, and the enemies are full of CC, you won't be able to do much. If you pick Khazix with an Orianna and a Yasuo, again, you won't exactly shine.
You need to communicate during champ select and before every fight. Ally picks Gragas? Pick Kha'Zix and ask him to ult between the carries and the frontline. Won't even have time to get shielded before you nuke them.
Ally picks Sejuani? Pick Ekko, ask her to constantly be in the middle of the enemy team and threaten the backline while tanking the frontline. By the time the enemies realize they've been slowed for slightly too long and they're out of position, you'll have stunned and nuked their entire team to death.
No balance changes are needed. I am usually one of the first people to complain when things are not well in terms of balance, but right now I could not be happier with the state of the game.
Let's see how I would go about the worst case scenario: the enemies have picked a mobile ADC such as Lucian, with Janna support and Lux mid. Can't get any worse than that. He can't die pretty much.
So, let's see. Out of the 4 Assassins I play, what can I pick?
- Despite countering Lux heavily, Ekko is not a good choice since they have too much peel and mobility for him to follow up. Ekko needs to weave in and out of combat, he can't afford to get kited and disengaged from.
- Kha'Zix is also not the best option against such a tightly packed backline that has strong burst. As long as Lucian or Lux are isolated and their big spells are on cooldown you can kill them even through the shields, but for that you need disruption.
- Katarina could work, since the backline is going to sit in a tight formation, as long as the enemies don't interrupt your combo or get the chance to shield everything. And for that, you need very focused allied CC. Not disruption but proper, clean CC. If your team has Leona and Malphite, go for it, and ask them to keep the backline stunned so that they won't react for at least 2 seconds- and they're guaranteed to be dead. Just press all your buttons.
- Talon, finally, excels at getting to mobile targets, but he really dislikes it if they get shielded cause he has long cooldowns. How do you stop the enemy backline from burst-shielding Lucian? Well, you either need a big threat to burn some of the shields and peel, or a big momentary disruption.
Now you see, momentary disruption does not mean an Orianna ultimate. You need something bigger, more messy and less focused. A Zac or Gragas ulti perhaps. Just enough time to blow up the target inside all the chaos.
Now, which would I pick?
Well, Ekko is something I'd avoid. Also, I generally don't trust the coordination of my teams, so I would not pick Kata since I"d have to rely on my team's CC way too much to be independent.
So, it's down to Kha'Zix and Talon. Both are great at getting to their target and they're OK with the enemy being mobile.
However, Kha can burn through shields with his superior DPS, but he needs Isolation and he hates enemy burst. Talon on the other hand doesnt care about burst or grouped enemies, but he hates shields.
So you look at your team: do you have a more organized team with clean cut CC like Naut or Amumu? Go for Talon. Do you have a lot of heavy tanks with disruptive CC like Gragas or Zac? Go for Kha.
Of course it depends on the lane too, for example I only play Kha jg and Talon mid, but I'm talking purely theoretical here.
Again, hone your strategy, hone your skills and your instincts, communicate well with your team and you'll never have a problem with an enemy squishy not dying.
{PS: Assassins specialize in killing ONE or maybe two targets, except for Katarina. Then they have to wait for cooldowns which means they are NOT meant to be primary carries. If the enemies don't have a super protected backline, you don't have to pick an assassin if you don't have good carries. A simple mage would suffice.}