Bankrupt companies do not hire people.
Exactly why you need to let them go bankrupt instead of propping them up, so other or new companies can occupy their places. But as long as bankrupt companies are using resources because they are being artificially proped up (bailouts, stimulous, ultra-low interest rates) there wont be a change and the capital structure will stay distorted and weak, because other or new companies can not take their place.
If we cut government jobs and let the private sector go bankrupt, what's left? I understand what you're saying, our current path is unsustainable. Eventually we will have to pay the piper. It's just not as easy as let everything go to shit and then pick up the pieces afterward. The risk that it turns systemic is rather high.
There is some true to this, specially in (and I believe only related to) the banking system. The banking system is a government created oligopolly and the government has regulated the amount and type of leverage they can achive. This has lead to a unsustainable situation. If we allow the market to correct it through the natural method (bankruptcy) the correction would be very quick, but also very brutal, with a lot of people loosing their savings, etc... I dont think this would be true in any other sector, IMO only the banking sector needs some kind of special solution. There are two sensible options.
1. What sweden did in the 90's. Its a government managed bankruptcy process. The government takes care of the banks for a while, so it can guarantee the deposits, but (and this is very important) completely wipes out the shareholders and the debtors. Both groups gave their money to a badly managed company so they deserve to loose their money. After a while, the government sells the banks to the private sector to recover part of the price of saving the banks. The BIG difference to what it is being done now, is that now we are rescuing the banks, including the shareholders and the debtors. The present "solution" is insane, its pure robbery by the plutocracy.
2. End the monpolly on money by removing legal tender laws, allowing to pay taxes in any currency, etc... By doing this you allow competing currencies and a competing financial system around these new currencies. This would allow for new investment to happen, that is now blocked because the banking system is bankrupt. Also, as the USD loses marketshare it would devaluate making the USD denominated debt easier to pay helping to solve the debt crisis much quicker.
I preffer the second solution as its better long term (the first solution does not change the present monetary system), but given what we have now the first solution would be very welcome. You can imagine we wont get any of both, we will keep saving the plutocrats through taxes and inflation, and will suffer stagflation for years until all the debt is wipped out and the capital structure has recover.