There are two main reasons people don't want government interfering in private markets:
1. The rule of law. No-one can be referee and player at the same time, and government officials should not be allowed to use their discretion to benefit one player over another.
With the Paulson plan, not only will there be discretionary action on a vast scale, but it also looks like there will be a minimal degree of accountability. This is not specific to the current plan however: any 'solution to the crisis' requires discretionary, arbitrary actions by the Treasury and Fed.
2. Government is inefficient. It is likely to make a mess of things and waste taxpayer money, so if something can be handled by the private sector it should be.
What I find funny with the Paulson plan is that instead of doing something to address this worry, it actually guarantees that taxpayers' money will be wasted. The fund is limited to buying worthless securities, so it doesn't even allow the possibility the taxpayer might turn a profit or even minimise the loss. It boils down to preferring to lose money instead of running a risk of losing money.
And what makes this even more remarkable is that the current environment is the best possible for government to actually make money by investing in financial markets. Following standard commentary, the biggest problem right now is not that there are gigantic losses in the system, but rather a lack of liquidity and a lack of trust. Government is the unique institution right now that enjoys an abundance of both, and in any economic system whoever controls the scarce resource is amply rewarded.
A plan along those lines, albeit one which I think could be improved, is described here. The Economist blogger's reaction is telling:
I get the feeling that a bigger hurdle to the latter plan than any real concern would be a gut Congressional reaction against the government taking equity stakes in a broad array of American corporations.
The Zingales plan also has much to recommend it, although it wouldn't be my first best option.
For my take on the long-term solution to the problems in the finance industry, tune in later this week.
Many (other) serious people think the Paulson plan sucks: see Naked Capitalism, Politico, and of course Tyler Cowen and Greg Mankiw.