Sony's best strategy for entering the pro camera market isn't to push the A-mount, but to play the long game and develop the E mount.
Mirrorless bodies (which may not necessarily be small) will displace SLRs. It's only a matter of time - maybe 5 years, maybe 10 years, but certainly within the forseeable future. The turning point will likely be 8k video.
Pushing the A-mount would be like entering the high-end SLR market 20 years too late. Instead, it would be better to concentrate on developing a comprehensive and high-end stable of E-mount lenses - everything from f/2.8 zooms to tilt-shifts, to UWAs, to supertelephoto lenses - while keeping ahead in mirrorless technology. Engineer the lenses not just for current E-mount cameras, but with the resolution needed to handle future bodies and the motor speed and power for lightning-fast AF when the bodies and their power supplies can keep up. Then, when technology catches up and the first truly action-capable mirrorless bodies hit the shelves, Sony will become dominant overnight, with a stable of high-end, suitable lenses, while Canon and Nikon would be stuck with a stable of lenses designed for SLRs (with a flange distance longer than needed for mirrorless) and years behind in mirrorless technology.