Why pay for an appraisal instead of checking sold listings?
In short: Sold listings tell you what some copies sold for. An appraisal tells you what your copy, in its observed condition, is worth for your purpose, and it gives you a document someone else will accept.
Sold listings are a good start, and I use them. But they mix conditions, include fakes and damaged cards described as near mint, and cannot tell you about the card on your table.
If all you want is a rough idea, check the listings yourself. You need an appraisal when the answer has to be relied on by an insurer, an estate, the IRS or the other side of a dispute.