This is true about privacy. I think back then it was not even private because you could literally point out the person who made that transaction considering the number of transactions. Like in the Block #170 or a few previous other blocks the input and output of mining is around 50 BTC with repeated bitcoin addresses. Let us say back then the whole world was watching these few miners doing their jobs they could easily tag the Bitcoin Addresses with the names and keep track ever after. This anyway did not happen but it was possible back then. In similar ways as they kept the tracking of Satoshi's address, it would be done for the others.

However, the reality is, the network has outgrown so much that even with the Block explorer you end up in the giant network of conformations and see thousands of them intertwined due to various destination transactions, output and input both.