Supercomputers could definitely do the job. It would have to have reasonably sized drawbacks though, I think that would mainly be the cost of the exotic components used to build the computer, the size of the coolers needed to keep it running - and by extension the slightly larger thermal signature, and the inability or very low ability to repair damage. This would allow for certain things while discouraging other things. For instance, you could mount guns on a platform to deploy as semi-permanent defense around asteroids being mined, or produce some very low-upkeep freighters. But, at the same time a true combat ship would work better with a traditional crew and large scale projects would need to be almost entirely crewed.
The fun would come in the mixtures, of course. If the computers counted towards crew while not requiring life support, then you could, for instance, put a large passive sensor buoy out in orbit of Pluto, with enough automation to keep itself running but also with one human occupant with supplies to last 10+ years, with the purpose of maintaining small breakdowns that the computer can't fix. Or, on the other side, have computer-assisted manned warships, bolstering their human crew with some computer aid.