In this scenario, the process of evolution we witness does have a purpose

That's not the same thing as acting purposefully -- which evolution would still not be doing in that case.

(I assume that we at least agree that for something to act purposefully, it must contain some form of representation of the goal to be obtained -- a thermostat at least meets that requirement, while evolution does not... even if evolution was as intentionally designed and purposefully created as the thermostat.)