I'm in favor of local no-burn laws, for approximately the same reason I'm in favor of laws preventing discharge of firearms except in designated areas or in cases of self-defense. My city is fairly densely populated and I'm not in favor burning down a couple city blocks.
Or the potentially toxic fumes as they toss
EVERYTHING into the barrel, to include stuff like plastics and clothing with flame retardants. It takes more to get them burning, but they'll burn nasty when they do.
but then they'd be tempted to steal each others recyclables.
Most of those recyclables cost more to dispose of than the plain garbage, so you might be surprised. Unless the city's paying a bounty per ton or something.
If you don't like it because you think the government is not doing enough to prevent littering, then may I suggest you reconsider your labeling? Removing a mandatory fee and creating a fee-per-use system where one may presumably opt out, opening the market up to competition and thereby incentivizing better services seems about closer to an expression of libertarian ideals than liberal ones.
The problem comes not from dickering between a company that wants $1.50 a bag and another that wants $2.92 for a can, the problem comes from people that like the $0 price of just tossing it out on some random street/highway. It's like illegal downloading; there's no way to catch any but a small fraction of the dumpers/downloaders. At least not without extraordinary cost.