If the owner still has equity, why don't they just sell it normally with an agent?

The bank does not block a sale after a notice of default. The owner can list and sell right up until the auction, and the lender is normally happy to be paid off. What the filing does is start a clock the owner can't stop, and that clock is the whole source of the discount.

Work your own numbers. Owed 180k, worth 260k. A normal listing takes time to prep, time on market, then 30 to 45 days for a buyer's loan to close, and any of that can slip. If the auction lands before closing, the owner gets nothing. Add agent commission around 5 or 6 percent, so roughly 14k on 260k, plus the arrears, late fees, and attorney or trustee fees the lender has piled on, which can easily be 15k to 25k by the time you're a few months in. Add the repairs a retail buyer's lender will demand. The 80k on paper is a lot smaller in practice, and it's only reachable if everything goes right on schedule.

An investor paying cash removes the schedule risk. That certainty is what the owner is buying with the discount. Plenty of owners do list, and plenty sell that way. The ones who sell to investors are usually the ones who ran out of runway, or whose house needs work no retail buyer will finance.

On credit: the missed payments and the default filing are already reported and stay reported. Selling stops further damage and avoids a completed foreclosure on the record, which is a heavier mark than late payments. It isn't erased.

One thing worth knowing early is that the equity you see on a site is usually just value minus first mortgage. Second mortgages, HELOCs, tax liens, and judgments all sit on title too, and a title search is the only way to know what's actually there.