In a lot of guides I see blink dagger described as a core item for heroes like Lion or Shadow Shaman, for initiating a fight. However these heroes don't have an AOE spell like Sand King, Enigma, Tidehunter or Earthshaker and by personal experience, when they blink among 5 heroes they get destroyed, being so squishy. In fact most of the time they don't have the time to cast hex or their ult. Do you think that it is worth buying a blink dagger, considering it is pretty expensive (half the prize of Aghs).
Blink dagger is an excellent item on both Lion and Shadow Shaman. Even if neither of them have big AOE teamfight spells, a blink dagger is still incredibly useful.
For instance, if both teams are fighting and your team is winning the fight, you can save the blink (i.e. not use it to initiate) and just use your spells as normally in the fight, then blink forward and pick off a hero when they start to retreat.
If your team is losing a teamfight, blink is great for getting away. This doesn't mean to abandon your carry at the first sign of danger, but if fighting is useless, it's better to not die and feed extra gold and exp to the enemy team.
Another strategy that is very good but requires excellent timing is to position yourself vulnerably when a teamfight is about to break out, then blink to safety when an enemy goes on you. This can make the enemy heroes waste stuns and get out of position, allowing your team to win the fight.
Versus Aghanim's scepter, I would say to prioritize blink on Lion every time, and also on support/mid Shadow Shamans. If your team is doing a push strat where Shadow Shaman farms the safe lane, then rush Aghanim's in order to take down towers early.
Both Lion and Shadow shaman have an hex which is an insta (no cast animation) disable. It makes the spell really powerfull especially versus lategames carries that have magic immunity (because you can disable them before they use their BKB, or any escape mechanism like Magina's blink or becoming invisible). With a blink dagger you can stay back (thus safe) and initiate instantly on an important target. Thats what makes blink on Shadow Shaman and Lion so important.
In most situation I would recommand to get a blink over an Aghanim because the initation potential increase a lot and is far more important than more burst. I concider Aghanim to be luxury on both of these heroes
For Lion a blink dagger is nice, so that you can initiate -> stun -> hex --> ulti your opponent. It not meant to initiate a teamfight. It more catching the opponent carry without letting him see you first. If an enemy carry, who tries to stay maximum time on lane sees you, he will probably move away. But if you blink and hex him + later stun him, your team can come in and has like 6 seconds to act. In this 6 seconds the carry can't do anything. Without blink dagger, he will see you at the same time you see him and move away. If the carry catches you first you can probably die from 2-3 hits and get stunned. so you can't do anything. Lion is a support hero, you mostly have some other hero to initiate the teamfight first like sandking, treant, magnus or enigma. As soon they did there stuff you cann still jump in from behind disabling the enemy carry or protect your carry, but if you are in the middle of that you die instantly. thats why a dagger is cool
And of course you can blink away if someone of the enemy team tries to catch you...
I think your initial premise is flawed. You're saying blink isn't good because you'll die if you jump into a 5 man team - that supposes that all the game is 5 man teamfight - which is obviously not true.
Blink on a lion, rhasta etc. gives AMAZING pickoff potential in lanes or 2-3 man groups. It completely turns the balance of power. Yes blink is expensive, but say you manage to get blink by mid / early game - around lvl 11? (Heroes like rhasta can regularly get it early due to tower push) - JUST three pickoffs on a carry / mid at that stage - takes you a LONG way towards lvl 16 + gets your team an advantage + pays back atleast half it's cost due to kill bounty. That's just the average / good case, not even the best one. You get it to pull farther ahead and stay ahead, and if the game is more even and down to regular 5 man - you don't necessarily have to blink suicide everytime - it helps a lot in positioning in a teamfight, 2 man impales instead of single - priceless.
And yes, if the opponents have a better team fight and group up early - you'll likely change over to force staff instead of blink and get that later if you hold off the early / mid pressure.