To derive her skills, let's look at the core concepts. Her Arts NP is a single-target NP that deals damage and has a chance to insta-kill the target while ignoring defense. That alone is the base we work on. To further elaborate on her damage, let's take into account her max non-Fou boosted attack of 8867 and her 0.9x damage modifier as Assassin. That brings her attack down to 7980.3 which is quite low. So, her damage on her NP is not really that high. But she can deny defense buffs so that's a situational boon.
Now, onto her first skill. She gains 1 turn of Invulnerability Pierce and 1 turn of Arts Up while debuffing her target with 1 turn of insta-kill chance increasing modifier. This skill strongly resounds the idea that it should be used when the player decides to use her NP because it makes no sense otherwise given that both Invulnerability Pierce and Arts Up are only 1 turn while the only source of insta-kill chance is through her NP. It also supplants the fact that it allows the player to have a 'failsafe' in case the NP fails to deliver the insta-kill. I can see that.
Next is her second skill. This is her only survivability tool and it grants her 1 turn of Dodge and 3 turns of Crit Damage Up. Looking at her stat chart, her crit weight is slightly above average (about +5 or so). So, she has a reliable dodge skill and an unreliable damage boost skill that either requires the other team members to be Casters or Berserkers to be more reliable or require the stars collected to equal about 35 or more in order for her crit to be more reliable.
Lastly, her third skill. It's an instant NP charge skill that grants 20~30% NP gauge at the cost of 1000 HP but cannot kill her. So, the way it works is that it hastens the demise of Shiki to accelerate her capability to use her NP. So far so good. Now, we must take into account that her NP charge per level is meager and the cost never changes when leveling up. So, what is it really meant for anyway? It's to allow her to reach 100% NP as soon as possible and to use her NP on her target. When taking into account her charge rate, you'll usually never use this skill unless you are backed in a corner and need a quick NP charge to hit that 100%.
So, let's sum up her kit. Chance to insta-death and def-ignoring damage NP. On-turn Invulnerability Pierce, situational damage up buff and targeted insta-death chance increasing debuff first skill. On-turn survivability buff with 3 turns crit damage up buff second skill. Instant NP charge with anti-survivability demerit third skill. So, from what I see here, she has a reliance on her NP for that insta-kill effect but has one (1) saving grace of that 1 turn Invulnerability Pierce and Arts Up that allows her to do higher than normal damage for that turn. Following it up, depending on whether you used her second skill on the same turn as her NP for non-NP crits, she will struggle to do damage until she gets to the second NP at which her 1st skill would usually be down (and third skill is used, depending on card shuffle). She thus loses her initial damage advantage of her first skill and have to resort to insta-kill to actually kill her target before they use their NP (if AoE) to wipe her out. She 'can' survive one more turn through dodging NP and attacks but that's mostly it for her and she fizzles away after.
So, losing her failsafe first skill, she would need to actually be able to follow up with lower than average attacks and her follow-up NP would usually be where she has no first skill for another failsafe so if her enemy has either Dodge or Invulnerability up on that exact turn before fizzling out, she's basically a goner who relies on her insta-death chance to do anything before she disappears to recover for the next battle. On top of that, having a skill that helps her survive but having another skill that reduces her survivability is counter-intuitive but they can work together at times. Sadly, the fact that she will die faster is not a foreign exception since she would have taken damage anyway along the battle and her survivability loss is only meant as a last ditch effort to do another NP work. Then again, going back to failsafe issue.
So now, why wouldn't I see that her kit is focused around her insta-kill aspect? Remember that her first skill still has a 5 turn cooldown to go through at max level. She would lack a failsafe method to deal damage to enemies who have survivability tools that are not Def Up and who can actually keep casting their protection every now and then because enemy Servants have no regards to cooldown.