The new emergency services network, or virtual network, is coming... But I don't think we currently have the sort of the phone coverage the emergency services need. LTE could provide that, along with high speed broadband for unconnected consumers, but it will be expensive. It's not been done so far because it's uneconomic.
I suspect what we will see is continued use of the Airwave TETRA system at least into the medium term with a phased introduction of LTE.
I don't think that's why Motorola have bought Airwave though. Motorola are in the frame for the user services part of the ESMCP. They'll be providing user management, applications and solutions for the end users. This is where Motorola Solutions - what used to be the radio part of Motorola - see their market heading, and where the money is to be made. What they need is an organisation of people who can interface with the emergency services - that's harder to build than a physical radio network. In acquiring Airwave they can ensure a smooth migration from TETRA to LTE in the UK. Other countries will be watching, and opportunities will form.
The future of the private TETRA network probably depends more on world events and the performance of the virtually private but ultimately public LTE network than anything else.