Specifically for Photoshop, when selecting multiple anchor points to delete, there must be a button on the 'Delete anchor point tool' options under Pen Tool to delete those selected points, or at least allow deleting them via the 'Delete' keyboard button without breaking the shape. So far, the only direct solution is to click 'Delete anchor point tool' and keep on deleting those anchor points one by one (but it sucks to do so on a very fragile and complicated shape with a ton of anchor points).
This can be done in Illustrator; however, it's necessary to be done directly in Photoshop too, without the need to back-and-forth from there.