Third-party DNS service occasionally creates large delays for users. When the original network is down, a user's browser will spend time on a useless connection attempt. Connection failures are much less likely to be cached than DNS failures. Third-party DNS service adds reliability risks. For example, some servers are running DNS software that can corrupt zone files, producing incorrect data for a large fraction of users, if the power suddenly goes out.
Extra servers mean extra chances for disaster.
Third-party DNS service adds security risks. Breaking the DNS protocol would have been somewhat more difficult and would have affected a relatively small number of clients. Third-party DNS service occasionally eliminates large delays for users. Without a third-party server, if a user attempts to connect to a misspelled name while the original network is down, the user will have to wait for a DNS timeout. With a third-party server, the user will receive an immediate error message.