Both law and accounting are subject to state regulation, so, at a minimum, work done remotely by non-licensed persons must be reviewed substantively and blessed by a local admitted professional before being shared with a client, and there are limits on what contacts with the client the back office can have.
In a legal context, the back office is limited to what a paralegal can do, and that varies considerably from one U.S. state to another, especially with respect to real property matters.
Mere "book keeping" as opposed to accounting is rarely a regulated profession under state law, but as in the case of legal services, the distinction between accounting that requires a license and activities that do not require a license varies from state to state (although less dramatically).
The notion of selling "forms" is well recognized, but what crosses over the line from selling a "form" to selling legal or accounting advice varies and can be treacherous.
I don't know off hand if this is true for accountants in most states, but in most U.S. states non-lawyers are prohibited from having an equity or profits based interest in a law firm, and referral fee compensation is also subject to significant professional ethics regulation. Non-competition clauses involving lawyers are also subject to heavy professional ethics regulations not common to non-legal professional activities.
Without a more concrete example of what the dropservicing business model would entail, it is impossible to do a very definitive analysis. Your model seems to be based upon obtaining services from a third-party and re-selling those services. For the most part, that isn't a workable business model from a regulatory perspective in the U.S. Instead, you need licensed "white label" providers as the face of the business and you may potentially provide services behind them in the back office.
There are some services along this line currently in existence with varied business models involving somewhat similar concepts: