Why in LT System Neutral is Solid Ground and Why Not in HT System?

1. How many 6.6kV hand-held appliance socket outlets are there locally?
2. How many single phase loads are connected to the 6.6kV?

To keep fault currents to manageable levels. By using a NGR the current is limited while the fault protection relays take over and cut the supply.

Pw's and Tony's answers give good reasons for no neutral but in addition HT systems are usually connected to transformers and these connections are delta and no need for a neutral.

on LT system were 3ph 4wire system (Star Connected on Secondary) is used, you need a solid grounded neutral and the neutral currents must be monitored by NEM with NER and the Adit relay, to trip your CB when your neutral current exceed the set value.

On HT System: is normally a Delta connected 3ph 3wire. but if there is any need for the neutral wire on the Delta connected TRNF, Neutral compensator can be used (and the above will be applied)

Look at my answer for the 33/6.6KV transformers.

As for the LV transformer, you do not restrict the earth loop impedance under most circumstances (it's against most national codes) due to the danger of touch potential to earth.