I think PBKDF2 may be better than Scrypt? Looking for someone to point out my logical error
There's no point in using either an ASIC or a GPU to calculate a single password hash.  That's true whether you use PBKDF2 or scrypt or Argon2 or whatever.

What massively parallel devices like GPUs or ASICs are good for is hashing millions or billions of passwords at the same time.  That's useful if you're mining a cryptocurrency or trying to crack a hash for which you don't know the password, but not if you're just trying to test a single user-entered password to see if if it matches the account's password hash or not.  For that, it's much easier and more efficient to just calculate the hash on the CPU.

Basically, what parallel devices like GPUs and ASICs do is give an edge to the attackers, who have billions of passwords to test and don't really care about latency (i.e. the time it takes for a single password to get hashed) as long as the throughput (i.e. the average number of passwords hashed per second) is good.  That's why modern password hashing schemes like scrypt or Argon2 are designed to make GPU/ASIC hashing as hard as possible, so that the edge they give to attackers over legitimate authenticators is minimized.

(And yes, a botnet of compromised personal computers could indeed be used to crack scrypt hashes.   However, especially if most of those computers had half-decent graphics cards, they'd be even better at cracking PBKDF2.)