The anti-libertarian arguments generally consist of these strawman caricatures, to avoid dealing with pretty much unassailable mainstream libertarian criticisms of major contemporary government policies, like socializing deposit losses with taxpayer-funded FDIC insurance, guaranteeing $1.5 trillion worth of mortgage backed securities every year through the GSEs, and bailing out banks that engage in high-risk lending practices.
The boring non-libertarian (political realist, non-radical) arguments about those are that doing the bailout is still better than the other possibilities. Also note that the bailouts tend to have positive financial returns to the government (because they get a lot of financial instruments at a very low cost, and then either sell them when they turn a profit or hold them to maturity, which again tend to be profitable because of low inflation in general).
Would it be better to change the current system so that the bailouts were unnecessary? Yes. And depending on the ideology of who you ask you get different wishlists.
Doing the bailout prevented the financial sector from being restructured through bankruptcy and market share reallocation. Systemically, it seems extremely implausible that preventing the normal function of the market, which incites good behavior and allocates capital to the best stewards of it, could ever be the right call.
The too big to fail financial market is already in a pathological state, it's too small, not enough competition, etc.
Yes, just brushing things under the carpet is bad, but whatever restructuring would have happened in that chaos would not have been an improvement.
It's unfortunately very much politics. For example see how the FASB tried to eliminate HTM accounting, but had to back down (and that chair resigned).
Yet! If the market already doesn't give enough shit to check the stuff in parentheses in a report for a 200B bank, then I suspect it's more of a theater than we like to admit.
Maybe the restructuring would have been chaotic, and undoubtedly would have been painful, but it's the only way to teach market actors to behave.
If Congress had gotten out of the way, other capitalized parties, like Walmart, were ready to step into the financial sector to add some much needed competition in the wake of the financial crisis:
