Convertible debt generally comes with a time limit, at which point it converts into equity at a pre-agreed upon price, just like if an angel had put a price on the round. That price is usually pretty low (good for the angel, bad for the entrepreneur), often lower than what it would've been if you'd just priced the angel round from the start. This is because in this situation the assumption is that you've tried to raise money from VCs and failed, implying the company has some problems that will prevent it from scaling.

In other words, if you seriously don't think you'll need to raise from institutional VCs, the standard convertible debt terms aren't for you.