Two people: it works
With two people a shared mailbox is genuinely the right tool. You can see what the other person has done, you talk to each other, and the volume is low enough that nothing is forgotten. Buying software at this stage is premature.
Three people: the first cracks
Duplicate replies begin. Somebody starts using flags. A convention emerges — move it to a folder when you have answered — and it works for about a month, until the first busy week.
Five people: it is failing and you cannot see it
This is the dangerous stage. The mailbox still looks under control because the visible symptoms (unread count) look fine. What has actually happened is that most conversations have migrated into individual inboxes, and the shared mailbox now holds only first messages.
Ask any five-person team using a shared inbox how many enquiries they received last month. Nobody knows, and that is the real diagnosis.
Eight people: something is lost every week
At this size, silent loss becomes routine: an enquiry nobody picked up, a promise nobody recorded, a complaint that reached one person who then went on leave. Each incident is attributed to bad luck. Collectively they are a system failure.
What to do at each stage
Two: nothing. Keep the mailbox.
Three: agree ownership out loud, and start measuring volume even if crudely.
Four or five: move to a queue. This is the right moment — early enough that migration is trivial, late enough that the team feels the need.
Eight or more: move immediately, and add service targets in the second month.
The migration nobody regrets
Keep the same customer-facing address. Route it into a queue instead of a mailbox. Do not import the archive. Give it three weeks with one firm rule: if it is not in a ticket, it did not happen.