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?"