For most small businesses the inbox is not a filing problem, it is a timing problem. The volume is usually manageable in absolute terms; what causes damage is that a genuine enquiry from someone ready to buy arrives in the same stream as supplier newsletters, delivery notifications, statements, marketing and the ordinary back-and-forth of existing jobs, and it can sit there for two days because nobody had a clear hour to look properly. The cost of that is invisible and it is real: the enquirer contacts somebody else, and the business never learns that it lost the work, because a lost enquiry leaves no trace at all. Nothing in the inbox indicates that the most important message of the week is sitting fourteenth from the top.
Classifying messages by what they are is a task that AI handles well, because it is exactly the kind of judgement that is easy for a person and tedious at volume. A new enquiry from someone who has not written before reads differently from a statement, which reads differently from a supplier's promotion, which reads differently from a message about a job already in progress. A tool can apply that distinction to everything arriving and mark it accordingly, so that the first thing seen in the morning is the small number of messages where a person is waiting for an answer, and the rest can be dealt with when there is time. The gain is not that less mail arrives. It is that the two-day delay on the one message that mattered stops happening.
The condition on all of this is that sorting must not become deleting, and the distinction is not a pedantic one. A classifier that is right almost all of the time is genuinely useful when the consequence of being wrong is that a message ends up in a folder a human will still look at. The same classifier is dangerous the moment it is allowed to remove things, because the errors are silent: nobody ever sees the enquiry that was filed as marketing, and there is no way to notice its absence. Sorting is reversible and its mistakes surface on their own. Deleting is not, and its mistakes are precisely the ones that never come to light. Label, prioritise and group as much as you like; keep everything.
That leaves a modest and sensible arrangement that a small business can actually run. Let the tool mark what looks like a real enquiry so it rises to the top, let it group the routine mail so it can be cleared in one pass, and keep a habit of glancing at the low-priority pile occasionally rather than trusting it blindly - which is how you find out whether the sorting is any good. And keep the replies to genuine enquiries human, at least in the first exchange: the fastest reply is worth a great deal, but the thing that wins the work is usually that a person clearly read what was asked. The tool's job is to make sure that person sees the message on the day it arrives.