How Fast Are Private, Govt Solutions?

I recently asked on Twitter:

When a problem is serious, and "something must be done", why do folks so often assume that it must be governments who do it? (more)

Many of my 113 gave a similar answer. A sample: 

Because if the private sector could handle it, they would already be doing so. (more)

If markets have not managed so far, they probably will not soon (more)

If something has become serious it’s highly likely it can only be solved by government or it would have been solved already (more)

If there were a market solution it would likely already have been done (more)

Because if it made sense for the private market to do it, it already would have. (more)

Because if it’s become a serious problem either the market was not able to or was not allowed to solve it (more)

But we could similarly argue that if the government could have solved the problem, it would have already have done so.

Likely the problem in question is not eternal, at least in its current form, and circumstances have changed enough to undermine prior solutions. Which makes this in part a question of rates of change. Once the problem changed into its current form, how fast was a government solution likely to appear, relative to a solution from non-government individuals or organizations? 

It isn’t at all obvious to me that governments are far slower to respond to problems. Once a few people start to complain about a problem, the number of complainers can expand very fast, quickly leading to calls for government action. Calls to which ambitious politicians might respond in only a few years, or even a few weeks. I have personally experienced just how fast mass-complaint-activated politicians can act; in my case, it was just one day. Private firms and philanthropists, in contrast, often take decades to respond to real needs. 

Another issue is that often current government policies are what slow or prevent private actors from dealing with problems. So a solution can be for governments to get out of the way, and then wait for private solutions to develop. More generally, many problems are best solved by ending or reducing something we have, rather than to adding or expanding something. 

Now when private solutions take longer than government solutions, one might give that as a reason for preferring government solutions. Yet none of my 113 respondents gave that argument. Many instead seem to assume that private solutions happen faster than public complaints can join into a call for government actions. A claim that seems just very wrong to me.