Actually Indian sold motorcycles with swing arm rear suspension in the 1910s. They called it a cradle spring frame, and it used leaf springs on either side of the rear wheel, parallel to the ground, on the upper part of the frame.
1914 Indian Hendee Special with leaf spring swing arm suspension
Cradle spring frames were an expensive option, and Indian quit offering them as an option in the early 20s.
I think reasons why swing arms didn't become widespread until the 1950s were because:
1. Swing arm frames were expensive.
2. The damping (stopping the suspension from excessively bouncing after hitting a bump) and shock absorption were poor. Until BMW's ISDT (International Six Days Trial - an off road riding event) competition motorcycles came out in 1936, all swing arm suspension used just springs, instead of oil filled or oil & air filled shocks. You can use a friction damping system (like was used in girder front forks with varying degrees of success) at the swing arm pivot to help control spring bounce, but you end up having to constantly adjust it, as the friction plates wear. Also, springs alone aren't that good for road compliance (they're either too soft, or too stiff/harsh for bumps of different sizes). Shock absorbers or hydraulic dampers in combination with springs work very well to overcome this issue. The thing is, most motorcycle manufacturers were small potatoes compared to the car manufacturers, so they they bought a goodly amount of components off the shelf, to save on the high cost having custom made parts pre-WW2. This was would have been thae case for shocks and hydraulic dampers (though HRD/Vincent did make their own hydraulic dampers - then again, their motorcycles were very expensive, so they passed the cost on to the customer). Almost all off-the shelf shocks were geared towards cars (and some airplanes), and as a result were too large and too stiff for motorcycle use.