Scammers would love that feature.... For privacy, it doesn't help if the user has email notification for PMs.
Okay, but in that case users would be free to refuse a PM of this kind to conclude a deal (it could be flagrant that the PM you receive will auto delete with a banner like we have for newbies PMs, for example), I'm personally not sure it would really make their lives easier (I could be wrong, but PMs don't seem to be the lifeblood of scammers here as most here block newbies' PMs).
You're right about the emails, although self-suppression of PMs here would still remove a potential vector of problems.