I agree there's that fundamental problem with the way email gets handled.
But at the same time I still wish Gmail would stop you from receiving emails on addresses other than the one you created yourself (ie by treating dots like any other character). It'd save me from getting several misdirected emails per day.
It's true that all these misdirected emails come down to people misremembering their addresses, but I think you're overlooking an important class of such misremembering (which can be addressed on its own).
I have a dot in my actual email address. There are several people who have a similar address who must be forgetting that their email address actually contains an additional initial or number. However some of these people do not have the dot in their actual email address.
I.e my email address: this.that@gmail.com
The other email addresses:
thisnthat@gmail.com, thisthat7@gmail.com, etc
...where the other addresses get misremembered as:
thisthat@gmail.com
I get these peoples' emails, but that could be easily avoided if Gmail took note of the dots.