Is there such a thing as auto crop?

Maybe this doesn't answer your question but my workflow is simply as following :

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I use crop with suppression of cropped pixels (not mandatory but save disk space) with help of the grid to correct vertical and horizontal alignments

And It is as fast as using rotation with only one operation

If you use the Straighten feature in the crop tool, it will do it automatically. Click the level icon and draw a line on the item you want to be straight.