This is an interesting idea but not a new one. I discussed it with officers when in our minority Administration in 2001.
The problem is, does one charge by bag or bin-load or by weight of rubbish? And what would be the administrative costs of such a scheme? To weigh each household's individual waste output each week or however often would require a revolution in the way of working of our waste contractor, SITA. In my street the common practice is for waste bags to be collected in a heap ready for rapid loading onto refuse vehicles with no regard being paid to the house of origin. Most blocks of flats - there are many in my ward and their number increases annually - use communal 'paladin' waste bins which sometimes accumulate rubbish block by block via a chute. Again a charge for individual householders would be very difficult to administer fairly.
If the Government is interested in pursuing this idea it will need to tackle these problems and others to make it worthwhile for refuse collection agencies to take it up.