After some testing, Dr. Charles West III is... inconsistent.
There are two main benefits to the doctor. The first is that he gives an additional hand slot, which can only be used for tools. This means you're trading an ally slot for a tool slot, and which encounters the usual problems of cards that take up slots for slots - you need extra actions to fill up those slots. Now, Seekers will effectively have a free hand slot, since most can justify running Magnifying Glass to fill it, and there are other useful tools that could be use - but that still needs you to spend more resources and actions to fill the slot, which is never great when your actions can always go towards investigating.
Second, on some successful investigates, he can exhaust to deal damage - but only on investigates that only succeed on 1s and 3s. This is two levels of specific - first, you need to succeed by 1 and 3. This is doable, but rather inconsistent - sure, you could use Steady-Handed to improve your odds, but it's hardly a guarantee, and Steady-Handed (and its other synergy, Chemistry Set) already encourages you to succeed by a certain amount. Second, this requires you to be at a location which has an enemy that can take one more damage.
There are very specific cases where he can be useful, but they require some fairly niche builds. If not for the differing classes, I'd be hard-pressed to find a case where you'd want to use him over Alice Luxley. His Science trait is the only notable one, and that's of limited use - he's not even Miskatonic, so he won't be getting any Miskatonic Archaeology Funding And with so many good Seeker allies available as is, you'd want a pretty specific place to fit the doctor in.