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You would have to try to forbid the spam via consensus rules, i.e. soft fork it out.
This would very quickly boil down to us choosing between having a flexible scripting system or not having spam transactions. Even if we restricted ourselves to whitelisting only specific single-sig payment schemes and forbidding all other transaction types, it would be possible to embed data in other transaction fields like signatures, public keys, or pubkey hashes. The trade-off seems rather unattractive to me.