One of my best friends runs a tow company in southern California and it can be very speculative if you rely solely on law enforcement impounds. First off, the number of tows can be impacted by the number of companies on the rotation list. If there are 3 or 4 companies, and you can keep up with the workload, it can be lucrative. If there are 10 or 12 in the same area, it can result in very few tows. Then you have to hope that the owners pay the fees, or, that you receive a significant amount at auction. In many cases the tow operator can be left holding the bag for scrap metal and this rarely covers the cost of the tow and the driver.
I agree that if they were relying solely on CHP impounds, their business model was flawed.
Also, I do know of companies that have employed people with felony convictions that had them reduced per PC 1203.4. Before the expungement, they were not able to do law enforcement tows and were limited only to private tows. AFTER the expungement, they were eligible. But! In the cases I know, the expungement was for drugs, not for the other crimes such as those that are crimes of moral turpitude. The key to the OP's issue is likely what the original offense was, and whether the offense was reduced to a misdemeanor, or reduced and dismissed.
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Ditto.
If it were clearly a big money win for the plaintiff, attorneys would be lining up to take the matter on contingency. I imagine the case is too speculative or would take too much work to make it worth the risk of pursuing it on a contingency basis.

