My mailbox (the physical one) disagrees with your claim. There are mechanisms to opt-out (at the cost of uglyfying my mailbox with highly visible label), but they are not banned.
In practice, no. The legislation has major loopholes, such as allowing unsolicited business-to-business marketing. And spammers still send junk to individuals with a disclaimer such as "This message is addressed to a business, if this is in error click here to opt out". And they seem to get away with it.
Neither of those represent threats to "privacy" in a typical legal sense. Both suck, but you're saying that you'll think the EU cares about car safety when they ban juggling.