Yes but it isn't so simple because if an airport can live off scheduled services alone, yet the bulk of its "security issues" (whether real or perceived) come from GA, they will just kick out GA.
That is how it works here in Europe. That is the sort of airport management which is present at
most places. It's the result of the "Univ of Upper Warlingham MBA" and "Masters in Risk Management" culture which has penetrated through Europe, and presumably the USA too but they have lots more safeguards there in GA.
Scheduled service passengers can be funnelled through a small gate, like cattle, whereas Bournemouth is a huge place, with countless aviation businesses around the periphery.
I've been there countless times and there are so many entrance points that the chance of a taxi driver meeting you at the correct one is very small
The saviour of Bournemouth is ultimately likely to be its huge commercial property portfolio which is mostly aviation related and needs airside access. The place will go bust if it ever relies on scheduled services.
If you let this kind if stuff get out of hand, you end up with say Gatwick, which herds scheduled services through cattle gates (where the security is easy to do) and where GA is handled by Harrods or Signature Handling who have set up £400+ cartels which have excluded light GA access.