I believe giving driver licenses to illegal immigrants would not make the DMV employees jobs easier, but even harder. For starters they would have to learn other languages in order to do the customer service job that is required of them. They would also have an extremely large amount of new customers that would fill up more lines and take more hours in order to process their information. They would also have to figure out how to send them the letters that would be addressed to them which would take even more time and more man hours in order to full fill the greater increase in service.
It would be a bureaucratic nightmare to have to figure out how to get licenses to illegal immigrants, as they come from countries all over the world. Identifying illegal immigrants would be difficult in and of itself, however what then stops an immigrant from picking up a new identity of a person living in another country. For example, one gets a license suspended, so assumes the identity of their relative living halfway across the world. This would be very difficult for the DMV.