Interesting Medium article, thanks for bringing it up to our attention.

Schnorr signatures don’t prevent spam, they would just make them less disruptive to the regular users.

Making spam less disruptive is not what I understood the Schnorr signatures to necessarily​ affect as a result, but rather to make those attacks more expensive which, of course, could eventually mean less of it.

Sam Wouters wrote:

Fortunately for us, Schnorr signatures would help combat this kind of spam attack. If we only have one signature per transaction, more transactions will fit into blocks and a spammer would need to send far more transactions in competition with more people, and thus likely spend more money to take up the same transaction space. Signatures are often the largest individual part of a transaction, so the attacker would be disadvantaged.

If the attacker chooses not to use Schnorr signatures and continues to use old signatures, then other users that do use Schnorr will still have smaller transactions to send and will thus have to pay less. This would still make an attack more expensive than before.

...but ultimately solutions would be found or perhaps the attackers would run out of money.