Economic institutions are not the same as economic functions. "Saving" and "investment" are economic functions. A bank is an economic institution that provides an economic function (bringing savers and investors together). But the function can occur without a particular institution, because alternative institutions can take its place.
The retained earnings of corporations are an example of an institution that could substitute for a bank in bringing saving and investors together. When banks were operating well, corporation ABC earning profits would often pay out some of those profits to its shareholders as a dividend. The shareholders would deposit those dividends in a bank, who would lend them out to corporation XYZ, who would undertake an investment project. Would the economic function be fundamentally different if corporation ABC reduced its dividend and loaned the funds to corporation XYZ directly? Or merged with corporation XYZ? Or invested internally?
You might observe that banks have close substitutes from competing institutions in some areas, but not others. You might say, for example, that banks are the only institution lending money for home purchases. But even if your observation were not exaggerated (employers often make home loans to employees), it comes from a time period when banks were functioning well. The real question is whether alternative institutions would bring funds to home purchases EVEN IN THE ABSENCE OF WELL-FUNCTIONING BANKS. I think they would. That's not to say that the world would be completely the same without banks. But the basic economic functions would still happen.
Democracy is another institution with an impact that has been good (I kinda like this free speech thing), but highly exaggerated. Operating the monopoly on force, and mediating between competing groups served by that monopoly, is a very important function. But a political institution such as election is only one way to serve that function. The possibility of ready institutional substitution for democratic political institutions is why democracies and autocracies have similar public policies in so many areas. It is critical that the basic economic function be performed, but there are multiple institutions that can perform it.