Faux Stone
Should you use a faux stone, a faux cement wall, a faux marble, or a timber look-alike porcelain tile that looks like what they are imitating but they are actually not what they are imitating?
You can argue about the notions of preference, technology, or economics, but the core issue of the question is about the intent: Why do you want something to look like what it is not?
If stress means wanting something to behave like what it is not, then, simply putting up something that is not what it is meant to be, means putting a whole new level of stressor onto your own space.
The problem with the spirit of place
A building material that travels a thousand miles to reach your household needs a better justification over a better locally sourced material that is not being used in the first place.
When a piece of wood, a pile of stones were being exported out of its region to be constructed somewhere farther away, the sense of place is disrupted by the alienation of other regions' material.
Unless place-design uniformity on a universal scale should be celebrated instead of diversity, there is no reason for one to travel from one point to another, from one region to another to experience the same living thing, culture, material, climate, and weather.
The Problem with not being aware of what you are doing
If being not aware is the case of committing something that is deemed wrong, so the next time, it will be alright to commit a crime (such as a bad design) the reason that you are not aware of something, and you can be wrong forever.
The comparison to the painting of a real thing
One importance of a painting is that it describes history like no words or voices is able to do. Imitation and expression can drive or excite your imagination.
All in all, communication between painting and you as art can move you.
But either way, as much as the concept of your faux stone should look like a painting, it normally does nothing like a painting but help something look like what it is not for no relevant reason.
The problem of wanting something you cannot afford
The great things in life often come not in the form of monetary luxury.
Visit the hospital bed or a cemetery and you will understand value, substance, or even regrets more.
When you are the user of the creation, you are the one who experiences the things in your spaces more than just visual level but the way things are being made.
If you know what is there is not what it is supposed to be, it will not become what you want it to be in any way. And why bother having something that is not what you wanted in the first place?
If you do not start anything with a good intention, a good design intention whether or not you are a designer, the chances are that the things that you will be associated with creating it or having it will turn out to be meaningless nonetheless.
What is not is still not what it is not.