You don’t necessarily need to store DNS changes into the blockchain. The blockchain will only keep the current state and would prune the changes. According to Diode’s blog posts, 20kb of storage is all it needs with BlockQuick, the newly developed light-client protocol.
The point is less about storing the audit history, but more about preventing Man-in-the-Middle attacks and solving the timestamp-certificate chicken-egg problem.
Yes, DNS-on-blockchain would likely make lookups orders of magnitude slower than they are now -- it's making a trade-off between security and performance.