Arguably, the government should be concerned, because it's hard to tax someone when you can't track their finances.
You can also follow the trail back arbitrarily far getting address after address. How does this net you anyone more information? How would you 'convert back' into a human name or address?
Something like the Coinbase merchant pages contained a surprising amount of information, and they were intentionally published.
You should probably assume that all businesses/exchanges with fixed addresses and traditional bank accounts will cooperate with authorities. And, some fair proportion of others, as well, including even those involved in explicitly illegal activities (who may be informants/plants, from the beginning or once discovered).
So if 'your' Bitcoin is received several hops from any of the known nodes/addresses, and after your spend goes several hops before arriving at a known node/address... you may be safe. That is, if you're small-scale, use Bitcoin only with others who avoid reporting requirements, and no big priority investigation peels back the links one by one using all the tools and pressure available to the state. And, if other security compromises and traffic analyses don't prematurely reveal your correspondent nodes.
But ultimately, a financial-enforcement agency might be running their own operation much like blockchain.info... with 1000X the resources, and various extra private sources of information. Every error by any participant -- mixing different outputs, client bugs revealing identity correlations, announcing pubkey-to-identity associations, matching time-online with time-of-spends, providing historic data after being targeted by an audit or prosecution, etc. -- would constantly improve the map of balances-to-real-world-entities. And like playing a game of 'minesweeper', a few lucky hits by enforcement, even years down the road, might suddenly illuminate large portions of the network. The blockchain never forgets!
And, a few policy changes could supercharge this map. Legislate that if you're an above-ground operation, you must register your public keys. Any balances received from unregistered/tainted addresses are subject to forfeiture (or a punitive excise tax), but balances received from registered addresses are OK. Bitcoin's public blockchain makes this possible, and it's not possible with cash.
All the above-ground businesses and users then register their addresses, and stop accepting -- or quickly report under penalty of law -- received funds from unregistered addresses. The gaps in the enforcement map then shrink pretty fast. You might also then have, within one blockchain, both 'dark' and 'light' balances that usually don't mix and aren't 1-to-1 interchangeable. To spend your 'non-taxable' coin on things like food or rent, you'd have to swap it for registered coin, through some legitimate-looking (and thus likely tax-paying) transaction. That's just money laundering, and it's no easier and probably much harder than with real cash businesses. (Are you sure the person willing to give you 'light' balances in return for your 'dark' balances is not and will never be an informer?)
The recipient could send the wallet's bitcoins to another address right away, but then the sender might as well have done that in the first place.
Still, in the rare case where you need an anonymous transfer from someone you completely trust, this might be the way to go.
From what I can see, its pretty much a statement of fact. A horrible fact, sure, but surely pretty much true. OK, given the numbers involved, its almost beneath worth bothering about, right now. But if it does grow, so will concern.
Government should be concerned from its POV. "We", me included, might well think, "well, sod them, ha, ha, cant get our money", and all that. But "we" would, right? Government, no matter how shitty, still has to look out of government interests. That's it job. Well, one of them, anyway.