(EDIT: To be clear I agree with you that that's the reason people often
think that AWS is cheap)
Yes, but that's a false comparison. It's cheaper to rent dedicated servers at any of several dozens large hosting providers than it is to use EC2 or S3, for example. For most people it's cheaper to rent racks and lease servers too (but depending on your location, renting dedicated servers somewhere else might be cheaper - e.g. racks in London are too expensive to compete with renting servers from Hetzner most of the time, for example).
It's extremely rare, and generally requires very specific needs, that AWS comes out cheap enough to even be witting batting range of dedicates solutions when I price out systems.
When clients pick AWS, it's so far never been because it's been cheap, but because they sometimes value the reputation or value the feature set, and that's a perfectly fine reason to pick AWS.
The point isn't that people shouldn't use AWS, but that if people thing AWS is cheap, in my experience it means they usually haven't costed out alternatives.
It's an amazing testament to the brand building and marketing department of Amazon more than anything else.