Isn't that dealing with the symptoms, rather than dealing with the cause?
Surely it is better to stop people littering, than pick up after them? Why should it always be someone else's problem - people should take responsibility for their own rubbish, including fag-ends, fast food wrappers, and apple cores (imho).
When I was up in Glasgow last year, they introduced anti-litter patrols (
link) (not because I was up there, the timing was coincidental

), because they were having to clear up 9 tonnes of litter some nights in the City Centre. An apple core here, a chip wrapper there, it soon adds up.