Can you be more specific than native English? I've never heard or read 'great cost' be anything other than large cost, it's the use of 'cost'. If you say 'a great price', sure, but 'cost' is already implying something negative I suppose.

(Native BrE, SW UK.)

Rarely trust native English speakers.

At a great cost is exactly at a very high cost, not "at a good price".

Any actual sources for your claim except for being a "native" speaker.

you 100% correct not sure why this is downvoted away