When a large amount of users are non-currency data users, currency users will face ... decreased ability to send free transactions.
There would be no incentive for a miner to process free domain name registration transactions.
Actually, the miner's incentive -- for currency or data transactions -- is in seeing free transaction space disappear so that transactions cost money. In a system where non-currency data transactions are encouraged, which clearly raises traffic levels (over a currency-only chain), collectively costing everybody more money.
Broadening the use of the Bitcoin chain strengthens it. If 55% of currency users generate maliciously, they can corrupt the chain. But if there are also domain name registrars generating, you would have to corrupt 55% of them too, and different interest groups aren't corruptible in the same way.
Yes, it strengthens the chain -- but if the bitcoin chain is processing (say) the majority of .p2p DNS records, currency users have to fight for space, paying higher fees to do so. Makes miners happy, and currency users unhappy.