First, as is mentioned already on this website, we strongly support recycling.
It is well-publicised that waste must be diverted away from landfill although this is a European directive hence the large fines that will probably be imposed on our government and that may be payable by local authorities (and ultimately us as council tax payers).
To address your issues:
Where from:
Supermarket recycling bins are very well-used, especially for glass which not all LAs collect from the kerbside. As you rightly say they can be utilised for items other than those included on kerbside collections. Packaging is a real issue - much of this is plastic film and rarely can this be recycled. In fact many people question why there is no end market for all plastics.
Food:
Maggot infestations occur even when food is wrapped. Flies may contaminate/lay eggs on waste food in the kitchen or kitchen bin or, of course, when the wheelie bin lid is lifted. Waste in the bins for up to 14 days provides the ideal conditions for the eggs to hatch and mature. The mature maggots then have to leave the bin to pupate which is why they are often seen on the inside of lids or crawling along garden paths (as happened in Bristol this year).
Rats:
Our council continues to collect side waste in bags. Combined with the promotion of home composting where rats have been found nesting in bins, householders believe these methods attract rats and mice to our properties. The rodent sense of smell is far superior to our own.
Value for money as far as council tax is concerned is a very hot topic. The extra cost of providing a weekly general waste collection is often exaggerated but obviously depends on the type of waste collection contract in operation. 75% of councils continue to collect waste on a weekly basis.
If people have extra waste to dispose of they must use their cars to take this waste to the civic amenity site. There may also be an increase in fly-tipping and/or contamination of the recycling bins.
Our main concern is the length of time between collections. 14 days is too long, certainly in summer months, for putrescible waste to remain uncollected.