Actually I don't think libertarians would argue that the problem is unsolved in both systems, they would argue that the problem itself is nonsensical. Most libertarians don't believe that non-excludable positive externalities are a problem, since it involves no harm to anyone and no violation of rights. They simply don't believe that because you indirectly provide a benefit to someone, you then have the right to coerce payment.

One could argue that there is an efficiency problem however - for example, take a bee keeper whoes bees benefit their neighbours. It could be argued that if there was some means to which the keeper could exclude those positive externalities, and there some level of payment at which the surrounding property owners would be indifferent between the excludable and the nonexcludable situation, there could be a Pareto-efficient gain. And since there is no reasonable way to exclude the benefits, it leads to the conclusion that the neighbours should be coerced into payment. Most libertarians reject this type of coercion prima facie.

Your spidey sense is failing you, you're making assumptions you've got no ground for. I've voted for left of centre parties all my life. I was born in the NHS and I'll probably die there too.