We are not saving Air France/KLM but their creditors

A firm in bankruptcy does not disappear, or even cease to function. Modern bankruptcy procedures such as the "Chapter 11" procedure in the US or the "mise en sauvegarde" in France are actually destined to keep the company's operations running with as little disturbance as possible and focus on financial restructuring.  The outcome of these types of procedures is normally a massive reduction in the firm's debt and a partial or total loss of ownership for the existing sharehlders. Often this is acheived by simply exchanging part of the firm's debt for equity, thereby turning an insolvent into a healthy firm with a stroke of a pen.
Because a firm is normally worth more as an ongoing concern than in liquidation, this solution ensures that value is no uncessecarily destroyed. At the same time it reduces opportunistic behavior, by making sure that all investors bear the full consequences of their decisions. Shareholders that have invested in risky ventures will lose their investment if these ventures turend out to be unsuccessful and creditors that have lend money at high interest rates to highly levered companies will have to absorb the losses.
Hence, there seems to be no good reason for why governments should bail out airlines or actually any company with massive amounts of emergency loans. The total sum of direct cash loans and guaranees invested by the French and Dutch government into air France amounts to around 12billion Euros. This is slightly more than the company's entire financial debt and should allow the company to cover operating expenses and reimburse loans for the next years. As a consequence, shareholders will maintain some of the value of their shares and creditors the entire value of their debt, which often paid high interest, given the risk that was correctly percieved but finally not absorbed by investors.
The direct consequences of these bailouts are obvious: By forcing taxpayers to subsidize creditors, wealth will be redistributed uwards, increasing inequality. For economists, however, this redistibuiton is not the principal prolem. As long as overall welfare is not destroyed it can be undone for example with appropriate taxation. More important are the many indirect effects, which will massively distort the allocation of goods and capital in the economy.
First guaranteeing the creditor's wealth but not the sharehodler's investment will make it more and more diflicult to raise equity for these companies. We have seen this effect with banks who have massive problems attracting shareholders. The consequence will be that companies adopt higly levered capital structures, which are known to create a large range of additional problems: Higly levered comapnies have no incentives to invest and might create uneccesary risk to "gamble for resurrection". Saving large companies will also have an detrimental effect on the allocation of captial across firms. Large companies with close connections to the  political system will be favored by banks and other investors, whereas smaller and less connected companies will be percieved as too risky. In the long run these distortions will lead to massive economic inefficiencies and low economic growth.

Suspending dividend payments would not only benefit the financial system but also bank shareholders

Banks’ quarterly earnings have been published and as expected the results are not pretty:  Provisions reflecting anticipated credit losses have increased dramatically, values of investment portfolios have dropped and only the frenetic trading activity of the last weeks has somewhat compensated this bleak picture.

Nevertheless, banks insist on maintaining dividend payments. This makes the US the only major economy where banks still pay dividends.  In Europe regulators have asked banks to suspend dividend payments during the ongoing crisis, and banks have duly obliged. US banks have made some concessions, such as refraining from share buybacks in Q2, but so far they have strongly resisted cutting dividends.

Why exactly banks refuse to temporarily suspend dividends during the time of the crisis is not clear. Some banks and commentators have framed the discussion in familiar class-war categories by opposing shareholders to workers and the society. Depending on which side of the argument you adhere to, dividend cuts would endanger the livelihood of poor retirees or force greedy shareholders to pay their fair share of the losses caused by the current crisis.

But this discussion is entirely misguided: We know that there is no direct relationship between dividend payments and shareholder returns. Every time a dividend is paid out the price of a share drops by exactly the same amount, leaving the overall shareholder wealth constant. As Nobel Price winning economist Franco Modigliani and Merton Miller have demonstrated, if a company’ operational strategy remains unchanged, dividend policy will not impact shareholder returns. If a bank does not pay a dividend, the poor retiree as well as he greedy capitalist can simply generate a home-made dividend by selling a small part of their shares, and obtain the same cash flow.

Information effects can sometimes make things more complicated, but these effects entirely depend on the context and can go either way: For example, a bank will see its share price go up, if it can convincingly explain to shareholders that the current crisis opens up a large number of profitable opportunities and it therefore prefers reinvesting profits rather than paying a dividend. 

While the effect of high dividend pay-outs on shareholder returns are not clear, the effect on shareholder risk is obvious and well documented: Banks with higher payout ratios have lower equity and therefore a lower buffer to absorb shocks, such as the one we are experiencing now. The scatterplot below illustrates that banks with high payout ratios in 2019 were among the worst performers in the current market crash.

Importantly, this endangers not only the bank and its shareholders, but the entire financial system. In the same way that irresponsible behaviour of non-symptomatic Covid 19 superspreaders creates a problem for all those who are being infected, high-risk balance sheets by financial institutions do not only endanger the bank itself and its shareholders, but also the health of other more responsible market participants.  If a bank fails, the risk can spread throughout the financial system and create a shock that overwhelms the capacities of regulators and central banks.

Governments waited too long to strengthen the health system against the virus storm and we are now paying a price for that; a financial storm, of significant severity, is likely to come and now is the time to anticipate it, strengthen the financial system and make sure that irresponsible behaviour by individual players is curtailed.