Well, to a point, you may be right. However, there many very large organizations that generally do better than the majority, so I don't think it's a linear or even necessarily causal relationship. Size certainly makes incompetence, inefficiency and corruption easier, and harder to eliminate.

There's also the problem of balance: several UN organizations, for example, do immense good with remarkably limited resources but occasionally they or their cousins fuck up really badly and cause severe harm. Because of the way our media (and our brains) work, we are much more aware of the fuck ups, but this is not necessarily a rational way to assess their overall efficacy.

I do think that the right has a small point in their perspective. It is almost certainly the case that being "the only game in town" does lead to a different set of incentives for public organizations. But I'm not clear that incentives are for worse behavior, at least not overall. Some parts of it are pretty complex to reason about - there's not a lot of potential within (local) government to get wildly rich, unlike in private corporations, but there's enough to keep small time grifters and scroungers happy. So it's certainly different from the private context, but better or worse is hard to say as a general rule.