Why does raising capital have to be so complicated? Can’t we just give our investors an interest in my company in exchange for their investment?

Taking investments is highly regulated, by both the federal and state governments. These regulations govern everything from required disclosures to whom can invest.
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Raising capital is a regulated process, so you cannot just give away an interest without taking additional steps.  In particular, federal and state securities laws, as well as a number of international laws and regulations, prohibit giving away ownership interests without either filing registration statements with federal and state authorities or ensuring that you fall into an exemption from registration (which themselves also require strict disclosures, certain filings, and other processes and procedures).  Failure to comply could result in significant civil and criminal liability.