If you look at recent mined blocks, a majority of transactions are still public. So yes, even if the default is shielded wallets and private transactions for a specific wallet, most of the chain is not using them.
True, but as of this month 30% of zcash transactions are shielded, and 20-25% of addresses are private. That's a fairly large anonymity set. The percentage of shielded transactions is also increasing, at a rate that will make them a majority within a year if the trend continues.