Does a lead-free solder have any advantages over solder with lead (other than the absence of lead)?

Yes, there are advantages in small feature surface mount PCBs. There are automated manufacturing processes that are designed to only use Lead free solder.
There are many solder formulations with a variety of metal ingredients which are created to satisfy production processes. For the most part the world of electronic manufacturing for consumer and automotive are Lead free. 
The reason why lead was -rightfully banned is just that the fumes are poisones and can cause an accumulation of lead in the body of the people who are involved in the production of PCBs. And as it is a “heavy metal” it should not be distributed in the environment.
I agree lead-free soldering got difficult but a hotter iron and special flux made it possible to live with it. And if you still think it is a must to use leaded solder - use an air cleaner even when doing hobbyists work. They are not too expensive and for your own health keep lead away from your body - e.g.

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