No need for publically funded sledge-hammers
If a communication is an incitement to commit an offence, an incitement to racial hatred, or likely to lead to a breach of the peace, then arguably the interests of the wider community are at stake, and prosecution at public expense may be warranted.
If the offensive message is defamatory or offensive to the person concerned, why does the public interest require the state to intervene? The courts have ample powers to settle disputes between parties - and the party affected can bring a lawsuit, and if successful, recover their costs.
There is simply no need to waster taxpayers money enforcing manners through criminal sanctions.