It’s simple, really:
An independent executor has to deal with the court much less often. Every time you deal with the court you are going to pay court costs and fees. For example, a regular executor has to get court permission to do even routine things, like pay bills. An independent executor can do these things without having to get a court order granting permission.
If you want to talk about really expensive, an independent executor can sell real estate belonging to the estate without a court order. A regular executor has to petition the court for permission, has to put an ad in the newspaper (that can be $300 by itself) and has to wait 30 days. All of this results in time delays, court costs, and in some cases a sale can fall through.