They might screw up?

I don't see a problem with this solution in this instance, but I have seen players decide to sub-contract almost all their runs and pocket the difference. It starts being a game of Middleman instead of Shadowrun.

Wouldn't the link be there every time you use the same equipment for a run? Do you expect the rigger to trade in every drone he used after every job? Or a mage to change his astral signature every run? The decker needs new icons every time and the sammy needs to get a new tricked out gun, too then.

Truth is, it would make having a shadow career impossible, unless you start thinking about whether the current owner of a piece of gear is responsible for every prior act committed by every prior owner. It makes it a lot harder to figure out who actually used it against a certain target. In todays world, guns have a habit of making the rounds. Even after being confiscated by the law, they have an uncanny ability to find their way back into criminals hands. I guess it depends on how much an sob you want to be. Yes, if the Demon Death Drone is used in a similar fashion a few times, it will draw attention.

As far as the original question, I think it is possible. It is not against the book rules to do so. But as has been noted, different people will react differently to the idea.

This was one of the ideas I was hoping to encourage in the Living in the Shadows campaign in the Welcome to the Shadows forum. So far, it hasn't happened.