Does an Instant Pot actually save time? For some time people have been making much of the Instant Pot as a time-saving tool. I recently bought one and it produces good results, but I'm not sold on it as a time-saver. Tonight, for instance, I made a recipe that involves a chuck steak and vegetables. In addition to the normal cooking stages, I had to allot time for the IP to come up to pressure and then for the "natural release" of pressure. At that point the time involved seems comparable to what I would have done on the stove. So is there any actual savings of time?

(Obviously it depends to some extent on what you're making.)
It is going to depend greatly on what you cook and where you are. Long braises can be shortened by hours. It is nearly impossible to cook beans in Bogota Colombia without a pressure cooker. cite

Lentils on the other hand. The recommended times in the IP manual and on the bag for not in a pressure cooking are the same. And as you say, with the IP natural release is not included in the time given.

Another time savings is not having to manage the cooking in the middle. Thanksgiving evening dumped turkey carcass, mirepoix and water. Set for 2 hours of high pressure. Ignore for three hours. Cool and refrigerate one gallon of turkey stock. No checking to see if it is simmering, adjusting the heat up, checking again, adjusting the heat down.