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Most rear wheels are dished to make room for the cassette. They have the drive side spokes comming into the hub more perpendicularly, which weakens the wheel against lateral forces in that direction. Something like this:

dished wheel

Why not have the frame be asymmetrical instead of the wheel?

asymmetrical frame

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    My first guess would be that it's to do with the relatively short distance between the bearings on the two sides of a freewheel hub, and keeping them relatively central on the axle. And then it's backwards compatibility from there onwards.
    – pateksan
    Jun 19 at 7:59
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    It also seems that with a dished wheel, it is easier to vary the amount of dishing and the width of the cassette/freewheel. With a dished frame, if you wanted to change the width of the cassette, you would need to either dish the wheel anyway, or "move" both bearings in relation to the centreline, therefore doubling the change to the spacing of the bearings/cones/races.
    – pateksan
    Jun 19 at 8:08
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    The mechanics of rim brakes on an asymmetrical frame may have also been a concern in the past. Clearly not so much of an issue these days, considering we're getting away with using disc brakes without too much trouble.
    – pateksan
    Jun 19 at 8:11
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    Related, maybe duplicate (but written from the view of the wheel, not the frame) bicycles.stackexchange.com/questions/66557/…
    – Criggie ♦
    Jun 19 at 10:10
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    This is already used by Cannondale since 2017 "AI Spacing". The disadvantage is potential increased Q-factor
    – Noise
    Jun 19 at 12:00

2 Answers 2

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They do exist, at least in concept. Here's a patent for the design dating from 2013.

https://patents.google.com/patent/DE102013217014A1/en

It seems to be a design element in some fatbikes too, purely because of the width of the large tyres used there.

enter image description here
From https://fat-bike.com/2013/03/fat-bike-101-frame-types/

This photo also shows just how far out the rear derailleur is with this design, well-past the centerpoint of the pedal. The rear mech is therefore more exposed to damage, so if you do this, consider a derailleur that "tucks into" itself more, or even an old-school bash-guard on your expensive derailleur.

Googling up phrases like "zero dish rear wheel bicycle" and "offset rear triangle bicycle frame" returned these three Specialised MTB frames from around 2010

Specialized has been rocking the asymmetrical rear ends on BigHits, Demo 8s and later P.bikes.
from https://www.leelikesbikes.com/specialized-asymmetrical-rear-end.html

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    judging by the picture, it looks like the primary concern is how to use a standard hub on a fat bike by shifting the hub to the drive side (look at the seat stay, that goes inside the wheel)
    – Renaud
    Jun 19 at 12:29
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    The frame in the picture looks weaker than the standard symmetrical ones, might need more material, and therefore more weight to acheive the same strength/stiffness. So "dishing" the frame maybe doesn't make the bike sturdier overall, it just moves the weakness from the wheel to the frame.
    – Robert
    Jun 19 at 16:31
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    Good point about derailer being exposed. Also the right chainstay would be more prone to rubbing the rider's heel.
    – Robert
    Jun 19 at 16:33
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A reason I would see is related to the cranks: a dished frame would require to have a chainring further from the center of the bike, which can be a problem from ergonomic and structural points of view.

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    Indeed, small people who need narrow stance width might not enjoy the limitation.
    – Robert
    Jun 19 at 16:36

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