Horses for courses
So what if Tetra has low bandwidth. That's not really what it is there fore!
Sure, some data and mugshots etc should flow through TETRA, but not floods of www, pron and iso images.
There are some very cool things in TETRA, like being able to make ad-hoc cellular style network connections on the fly. GSM, otho, is pretty good for putting in a static coverage area.
There are very good reasons for having private networks for emergency services:
(1) preventing congestion. Last time we had a decent eathquake here, the cell system and landlines were choked for the next 30 minutes by everyone phoning their friends: "OMG! did you feel that!". If emergency services had needed GSM to do anything they'd have been SOL. Likely a big bomb or other event triggers the same reaction.
(2) independence of damage to cell systems.
So why not give the plods both? That way if GSM is available they could use that and TETRA when not, or vice versea. It is even conceivable to put both in one handset and to bridge between the networks so that it is all seamless and plod-proof.