All of it could have been done just the same, but in return for 100% equity in the failing banks assigned to the governments. The existing shareholders of failing financial service industries should have lost everything.
I don't think that would have hit the people you want to hit. The shareholders of financial institutions are overwhelmingly not employees of the financial institutions. In 2008, Citigroup was 84% owned by institutional investors, meaning pension funds, mutual funds, insurance companies, etc. And the biggest owners of mutual funds are 401k accounts and IRAs. I couldn't find any numbers on how much financial institution stock is owned by various sorts of retirement accounts, but it's a lot, because retirement accounts own a huge chunk of stock of all sorts.
Your proposal would have pushed pension funds and insurance companies toward insolvency and further damaged the retirement savings of tens of millions of ordinary middle-class Americans. The bankers would barely have been touched. They'd have lost some, sure, but much of their compensation was in the form of lavish bonuses, and many of them regularly cashed out their equity positions to diversify and to avoid ownership thresholds that trigger greater SEC scrutiny of transactions. Insider ownership of the major banks in 2008 was less than 1%.
The equity should have been forcibly reassigned, as the capitalist system only functions properly if losing players actually lose. It's what makes risk undesirable enough to give rise to a risk/reward equilibrium.
This is the moral hazard argument, and it definitely has merit. But this is where we get to the "too big to fail" part of the problem, which wasn't only that the participation of the banks is essential to the operation of the economy, but the ownership of those banks is also essential to the structure of the economy.
It's worth pointing out that although I described the bailouts as "loans" that's not technically correct. What the government actually did (except for AIG) was require the institutions being bailed out to sell the government a large chunk of newly-issued preferred stock. This positioned the government ahead of the holders of common stock in any bankruptcy proceedings, and gave the government outsized voting rights. The preferred stock also paid dividends, starting at 5% and rising to 9% (this is the reason most of the preferred stock was repurchased ahead of the planned schedule; the rising dividends would get punishing). Citigroup took a slightly different approach, repurchasing shares of common stock and swapping them for the preferred stock -- which actually did result in the government holding a 34% ownership stake in the company at one point, the largest shareholder.
AIG was handled differently. They were in a worse negotiation position so they ended up giving the government a large tranche of preferred shares that were convertible to common shares, and provided voting rights and an equity stake equivalent to 79.9% of the company (the government chose 79.9% deliberately because 80% would have triggered some messy tax rules). That enabled the government to fire and replace the whole leadership team, which they did. But they didn't take shares from anyone; all existing shareholders kept their shares, although their value was diluted to about 8% of what it was after the price crashed, so a fraction of a percentage of what it was before.
Arguably, what happened to AIG is close to what you wanted, and AIG was the holder of most of the credit default swaps that were at the heart of the problem. But doing the same thing across the board to all of the banks, including the ones who didn't want or need bailouts but were forced to take the money (for good reasons), would have been incredibly destructive to the economy in general and retirement savings in particular, and deeply undermined trust in the banking system. Exactly the opposite of the intended result.
All of that said, moral hazard is a real concern. Investors must face actual risk, or capitalism doesn't work. I'd argue that they did face actual risk; lots of portfolios were wiped out. 2008 severely sabotaged my parents' retirement. I don't think the fact that it was only a 99% loss instead of a 100% loss is the difference between capitalism working and not, though, and I think it would have been politically infeasible for the government to deliberately inflict further losses. There was also no legal/procedural way to do it. That was fixed in the 2010 Dodd-Frank Act... so now the government does have a way to seize and even liquidate even the largest institutions -- though in practice huge holding companies like Citigroup are insanely complicated so even with the legal tools do to it, that might not be the best option.