Can cryptocurrencies be ANONYMOUS and have Anti-Money Laundering safety at the same time?

So I am just a newbie and I am just beginning to learn about cryptocurrencies, but like most of us I had heard about Silkroad and all the crap that happened making everyone not trust Bitcoin as a viable option. But it seems it has made it through all the bad publicity and yes it's still going strong.

I wondered about safety and just how anonymous was the blockchain. In theory it seemed ideal because it was not centralized and so many miners had a 'copy of the ledger' so to speak. I did some research and found that according to http://www.sciencemag.org/news/2016/03/why-criminals-cant-hide-behind-bitcoin

a husband and wife team named Philip and Diana Koshy were grad students at Penn State in 2014 and were able to map IP addresses to more than 1000 Bitcoin addresses. (here's a link to their published work: https://pdfs.semanticscholar.org/c277/62257f068fdbb2ad34e8f787d8af13fac7d1.pdf)

Mapping seems to be the terminology for this work and there is one company that I found that says that although they don't believe Bitcoin will totally replace the current system, maybe they can provide some level of confidence for financial institutions to use cryptocurrencies. Here is one video I watched with Dr. James Smith, CEO and co-founder of Elliptic.co

(*note -the thumbnail is showing a different speaker at the conference)

This is so fascinating to me and I am one of those that still believes that cryptocurrencies should, could and WILL replace the current financial system.

~LoveWave