Yes the 51% miner could attack with two alternating chains as you describe but I am not sure what the advantage is from the attacker's perspective.
Given 51% or greater mining power, the attacker can simply mine it's own chain with whatever transactions it wants to use and it will as a matter of statistics get ahead of any other chain that the remainder of the mining community can produce.
It is this ability to get ahead on the chain with valid proof of work that allows that attacker to always get long term control of the chain and fork it in the direction the attacker wants to go.
The attacker could choose to include all other transactions (good behavior), double spend (fraud), filter out particular transactions or transactions from particular address(s) (targeted denial of service), reject all transactions (complete denial of service), long term reject block solutions from any subset of miners (monopoly)
So the question back to OP is, "What extra advantage does the dual chain attack he describes give to the 51% attacker?"
I think the difference is that it would be more useful to an attacker who really didn't want to gain anything from the attack other than making bitcoin completely un-useable. The typical example is a government who just wants to shut down bitcoin, doesn't really care if they gain anything in the process. This would make all services built around the bitcoin blockchain very unpredictable and impossible to use.
Another difference is that this attack would not be preventable by Gavin's "chain with more priority" idea (
http://gavintech.blogspot.com/2012/05/neutralizing-51-attack.html). The standard 51% DOS attack where you just mine on your own chain and don't include anyone elses transactions would cause the attacker to lose 'priority' (coin age destroyed). But in this attack, the two chains would have roughly the same priority (coin age destroyed), so you couldn't prioritize one chain over the other.