Well, that would look like heck. Have you checked to see if the electrical and/or gas are getting in the way.
I just checked our stove - it sticks out about an inch. It been like that for 25+ years. Life does carry on.
I’ll guess that Lenaitch missed “wall” in the title, which you didn’t repeat in the post itself. In answer to your question, it depends if it’s a load bearing wall. If it isn’t, cutting into the wall is a solution, but you’ll need to consider the routing for supply lines. If it is load bearing you’d need to think about it and be sure of the result before you do anything rash.
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