I don't pretend to hold a crystall ball or magically see the future, but arguments could be construed why it would happen:

Let us consider a spectrum of splitting differences, and their extremes:

Consider a factory that runs 3 human shifts, and N full-time labour positions.

In one extreme the company buys for each 3-human-shift position a single robot price.

In another extreme, some workers decide to buy a robot on their own, and hope to send it to the factory.

Now consider 3 robots are bought per 3-human shift position, i.e. one robot corresponding to each human worker. If the robot follows the worker home, it would spend 2 / 3rds of the time at home, and one third of the time at work. So a company could pay a third of each robot for 3 shifts. What is won by whom?

The companies:

1) paid the same amount of money

2) don't need space to store a large stock of backup robots (suppose your robot broke down and needs a few days to get repaired, the company can ask your colleagues from other shifts if they want to rent out one of their robots, so instead of having 2 robots in the household, some will only have 1 for a few days and they will get compensated by whoever was responsible for the damage, if it occurred in job related conditions or leisure conditions)

From the perspective of the employees:

1) Instead of paying 100% of the robot price, you only pay 66.6%

2) Instead of blindly hoping to find an employer where you can send your robot for work, your employer is organizing this for you

From the perspective of the robot makers:

1) Sales triple

2) gather real world data 3 times faster than robot makers not participating in this type of scheme

3) just like the factories, having a larger base of robots means the shot noise on the stream of incoming robots needing a repair is buffered, so capex on the repair centers decrease

From the perspective of jurisdictions, power blocs, and robot warfare:

1) Your economy learns 3 times as fast compared to blind ideological jurisdictions that believe the optimum must lie at the extremes: either company buys 1 robot, or 3 employees each buy their own robot

From a different perspective one can argue much simpler: we already see this in action with company cars, robots for human transportation operated for work part of the time and operated for leisure in the rest of the time, complete with myriad of rules and regulations to determine who pays for repairs and how or when the damage was incurred.