With a cpu-only coin, you could mine with your existing computer and with stronger anonymity, you could do it without anyone tracing you. So what do you think will be the most popular way to obtain crypto-currency.

I can think of smart metering and authorities quickly recoginizing your "unnormal" energy consumption. So mining a coin and using quite a lot of enery 24/7 could quickly be traced ?!
Couldn't that become a problem with the proof of work concept?