the Gardai don't engage in a criminal investigation on behalf of a private individual. So you'd only be paying a small share towards the costs of criminal investigations.
Not on behalf of a private individual, but on behalf of citizens of the State, as you acknowledge.
If I report to Gardai that I have been assaulted they are duty bound to make inquiries into the matter and in doing so, if satisfied that a crime may have occurred they will open an investigation into the matter. I don't have to pay for this in addition to the taxes that I already pay for the provision of this service to others. Not even a small share towards the cost. To implement such a measure risks serious crimes such as assault going unreported.
Utilities are a very different matter and paying based on consumption leads to much more less waste
This is debatable. Personally I see little material difference in the waste that I produce now than say 5 or 10yrs ago. Most produce I buy comes in the same packaging that for the most part has not changed over this timeframe. The only notable exception I can think of is the plastic bag levy which has certainly reduced my usage of plastic bags. To such an extent, that were the levy to be removed I could not envisage myself returning to using the mass amount of plastic bags as before.
Certainly I compartmentalize my waste into general waste, recycable etc, but I am still producing the same level of waste.
Specifically with water, there is also little to no evidence of this.
As I already pointed out, household consumption of water is almost exclusively of necessity - washing, cleaning, cooking food, quenching thirst.
Over indulgences may include filling too much water in the kettle for a cuppa, or someone spending long bouts of time in the shower. But in the round there is little to zero evidence that these 'indulgences' will change with the onset of charges.
Unless of course, charges were set at draconian rates (to be defined by your own level of income), but doing so to save the water on a few cups of tea is an absurdity in a country that has as a natural resource an abundance of water.