The business case for distributed compute is not a big mystery.
If this team were to try and do the compute themselves, they would have to compete with existing traditional datacenters. Since SONM have no technical advantage over a traditional datacenter, they would not be a able to compete if they built their own dc.

Look at the similar project DBC (DeepBrainChain), which is developing ditributed AI mining. They mix this up with an investment token (DBC) and a big ICO. Probably just to secure their Lambos in case the distributed compute doesn't work out. Recently, they got this brilliant idea to make even more money by bypassing the distributed concept and play on the greed of miners/investors. They are selling pre-built, very high end AI hardware and hosting services. They give priority to people with big DBC holdings. Basically, they are building a high end traditional datacenter with other peoples money. No economical or technical risks and they can start computing before they solve the distributed compute problems. They have sold thousands of AI compute machines this way. (Way higher spec than 1080 Ti).
Chinese Entrepreneurship at it's best and maybe the only way to do the "mine for themselves" and compete successfully against traditional datacenters.

The distributed model competes by externalizing many of the costs by utilizing the scale of "mining as a hobby". Hobby miners don't count all their work hours as a cost. They don't always count all the hardware investments as cost. At best, they make some initial ROI calculation and make sure the income is greater than the cost of power. This has proven to work long before Bitcoin saw the light of the day. It started with SETI@HOME and then BOINC, which is now the largest super computer cluster on earth. Those projects didn't even have economic incentives.

The big technical problems to solve are related to security and hardware bandwidth. BOINC and other distributed computing have solved this but it is significantly less real-time than POW mining. Long lasting work packages and verification times in centralized systems is the state of the art. Typical low bandwidth mining rigs are not ideal.