Background
There are times where I feel like a certain spell would very much suit a certain character or concept, but because it's not on that classes' spell list, they can't have it.
The classic example in my mind is that Tempest Domain Clerics can't have Storm of Vengeance (even though it used to be on the Cleric spell list in previous editions) or Whirlwind or other spells that suit their theme. As it stands, you'd need to take 17 levels in Druid (or 18 levels in Bard for their last use of Magical Secrets) to get those spells, at which point you're not really a Tempest Cleric anymore, you're a Druid or Bard with a dip in Cleric.
I wanted to come up with a way to allow certain classes access to certain spells that they otherwise can't get. I thought a feat might be an acceptable cost for this benefit (aside from a DM just saying "just have the spell anyway" or "I say that this spell is on the Cleric spell list for my games", etc).
Proposal
My proposed feat would be that, if you have the Spellcasting class feature (i.e. you are of a class that can already cast spells) or Pact Magic (because Warlocks spellcasting class feature isn't called Spellcasting), then you can gain access to one other classes' spell list and "they are X spells for you" where X is your spellcasting class (if you're a multiclassed spellcaster like a Bard/Sorcerer, then pick one of your spellcasting classes).
So for a Cleric gaining access to, say, Bard spells, the Cleric would use Wisdom rather than Charisma; this idea is based somewhat on the Divine Soul sorcerer, who has access to all Cleric spells but uses Charisma to cast them.
Question
My question is: Is this balanced? If this is overpowered, would restricting it to only a school or two from the other spell list help to balance it? If this is underpowered, I'd probably throw in a +1 to your spellcasting ability to help balance it. Or is this so broken in a way that I haven't anticipated that I just shouldn't do this at all? Perhaps this is something that is only unbalanced if Warlocks are included (so simply excluding them from this removes a bunch of balance concerns)?
Also note that, although I've recently asked questions about Rangers using the Wizard's spell list, this is actually nothing to do with that. However, I am currently assuming that Paladins, Rangers, Eldritch Knights and Arcane Tricksters are to be included in my proposed feat. Any or all of these can be excluded as I suggested for the Warlock above if this is unbalanced.