Doing markers in other units is probably technically possible, but not advisable or practical.
The main advantage of pixels as a measurement that the symbols remain the same size as you zoom in and out (change the scale).
If you choose meters or degrees, this doesn't happen. When zoomed into a town, a degree-sized symbol would be larger than the screen.
If you use (for example) 10km as the marker size, these would be dots when fully zoomed out. So you'd need to change the size for each zoom level.
A second issue - specific to degrees - is that a degree of longitude is longer near the equator than at the poles. This means your symbols will shrink or distort the further away from the equator you are.
Add to this the fact that you'd need Leaflet to do all the formulae for each marker, and account for zoom level/scale, it's probably best to stick with pixels :)