The clarifier requirement (frequency fine-tune) for correctly receiving SSB is why scanners generally don't bother with SSB. Getting it adjusted so received voice has correct pitch is not an easy process to automate. Plus, you'd have to modify the scanner PLL to adjust in maybe 10Hz increments instead of 2.5KHz increments. The manufacturers probably figure it isn't worth the extra expense and hassle for the limited demand for SSB RX.
While there are no scanners per se that do sideband, radios like the recently discontinued Icom R20 and the AOR-8600 do.
The other side of this coin is that most scanner antennas are rather inefficient in the CB band. With just a little whip on the R20, for example, your chances of hearing anything are very slim. Better with a discone (but even there, not very efficient).