Two jobs sit behind this, and most tools blur them into one. The first is adding a picture to a page that did not have one: a logo on a letter, a photograph in a report, a scanned signature block. The second is swapping a picture that is already there for a different one — usually a logo that has been rebranded, on a document nobody has the original layout file for any more.
They need different behaviour. Adding means placing something, so a ghost preview follows the pointer and you see the size before you commit. Replacing means taking over an existing position exactly: the new image inherits the old one’s place and dimensions, so the page after the swap is identical apart from the picture itself. A tool that treats replacing as delete-then-add gets this wrong, and you spend ten minutes nudging a logo back to where it already was.
Extracting is kept separate from removing for the same reason. Pulling a photograph out of a document to use elsewhere is a copy operation and leaves the page untouched; taking a picture off a page is a deletion. Merging them means somebody eventually loses an image they only wanted a copy of.
Cropping happens on the page, with handles on the picture at the size it will be printed. Cropping in a dialog with percentage fields is a guess followed by a check, and usually two or three attempts.
One thing worth pointing elsewhere for. If what you want is a logo or a word on every page, this is the wrong tool — placing the same thing nineteen times is what the watermark tool exists to avoid.
Everything runs in this browser, nothing is uploaded, and your original file stays exactly as it is until you download a new one.