Disagree. I think Nightingale is fine at Tier 3. The reason why she isn’t any lower is because of her powerful targetable Buster buff (50% at max level, for 3 turns, on a 5(!)-turn cooldown), her powerful targetable heal (on a short cooldown too), and because her non-damaging NP serves of a (despite niche) great utility in some CQs and against certain fights. Think about this, against enemies with buff removal before dealing damage with their NP like Amakusa or Abby (even if she’s a Foreigner), Merlin’s party-wide invul, Irisviel’s party-wide guts, or even David’s or Tristan’s party-wide Evasion, and all of those self-protection skills won’t save you from taking all the damage. So there’s two options: draining NP gauges or reducing their NP damage and ATK considerably (basically debuffing the enemy). Nightingale is one of the few Servants who can do the latter effectively… If she can survive.
That’s her main issue: Nightingale would be a top tier Support if not for her glass canon class. However, her Berserker class and 2nd skill help her deal some damage if she’s not serving as a support, until she can. So I think Tier 3 is a great middle place for her. Her Berserker class is also useful in a way, because you can equip 2030 on her and she won’t keep all the stars for herself, like Rider supports or even Casters sometimes. So, you’re able to get guaranteed (Buster) crits for your DPS.
However, in the future, there will be ways to make her survive a bit longer. Reines, removing all types of class disadvantage, can help her survive some more in longer fights.
So yeah, I think Nightingale’s placement in Tier 3 is decent. She’s good, not overpowered, but definitely not bad. And even less useless. She has a niche and a use, and she does it well. You just need to… Well, help her survive, ironically. Her 2nd skill (and her 1st, if you decide to use it on her) can definitely help with that, though.
Edit: in the future, she gets a skill upgrade that even gives Debuff Immunity on her targetable healing, if I recall correctly. I’d haveto check later. Either way, it’s definitely useful and a nice extra.