It's actually technically more demanding in ways to have a duplicate model mimicking it. It would require having at least some of its own data.

Rendering a live mirror is the exact same thing as rendering the game twice. So of course taxing, but well within reason for computers since the early 2000's.

You don't need extra vertex data or anything of an extra model you simply need to run a second calculation based on what a camera would see reflected on the other side along the plane of the mirror. The exact same calculation you just did for the basic render.

It's how portal did the portals. Just run the viewing calculations for each individual aspect you want.

You could have a set of televisions in a game all separately rendering different rooms using the exact same concept. Which I would bet is present in five nights at freddy's

In fact some games even do this for the mini map. Just do a pulled out low vertex shot of the whole map with really simple lighting. Gives a great mini map. Same concept as rendering a mirror. Like in Skyrim.

It's just a pain in the ass frankly. Why go through the massive headache for a throwaway barely important effect. Cut the corners and leave it up to the players suspension of disbelief.

It's not overly taxing to make reflections, it's often conceptually not worth it.