Your description is apt when you are talking about an analogy between technical debt and personal debt.
For companies, whether to use debt or equity to finance their balance sheet is just a technical decision. Either way, you have to pay the cost of capital.
(Ie even if you finance your project from equity and not from debt, it still has to be better for your shareholders than just giving them the necessary capital back via a stock buyback.)
A company can have debt as a permanent feature of its balance sheet, just like equity.
Funny enough, I suspect from a corporate finance point of view, technical debt should actually be called 'technical equity', because technical debt only gets expensive when your project takes off. If you never end up using that piece of code, the technical debt never has to be paid. But it gets more and more expensive, the more successful your project is.
Just like selling 50% of your startup to an investor (as equity) gets more and more expensive (in retrospect), only if your startup really takes off. Debt stays the same price, whether your startup is middling or goes to the moon.