I’ve noticed that on upright pianos, the keyboard is off-centre. That is, there’s a space at each end of the keyboard, between the last key and the side of the piano, but the space on the bass side tends to be wider than the space at the treble side. There’s usually room for a mug on the bass side, but not on the treble side.
It would seem more logical to have the keyboard centred.
Is this pattern simply so I can have a mug of tea while I’m tickling the ivories? 
Weird, I never noticed this before, but you’re right. My upright piano has a few cm extra space on the left!
Each key action is fairly compact, so that’s not it.
My guess is that it’s to accommodate the bass strings. The longer strings mean that the case has to be either taller or wider, and a taller piano would mean that the hammers would have to be taller and might not work as well.
The una corda and sustain foot pedal mechanisms run through there. The extra space is also used by the lowest bass strings, but that isn’t a strict design necessity.
ETA: Here’s a picture.
I think, and this is going on extremely fuzzy memory, that the strings on an upright are not vertical; they slant to the left. Which would mean they need a little extra room on the bass side that they don’t need on the treble side. You might try opening the front panel as if you were going to tune the old fellow and verify this.
ETA half right, anyway.
If the dimensions of the case and placement of the keys was symmetrical/even when viewed from the outside, this would mean the music-making part of the piano, where sound comes from internally, wouldn’t be? Is that the gist of it?
