A non-parallelizable proof of work scheme has the consequence that nobody can become stronger than a, say, 4.5 GHz overclocked single core pentium. This is what we want.
And bitcoin gets taken over by a single botnet.
To my current understanding this is
just the other way round.In Bitcoin, a single botnet can obtain so much hashing power as to take over the system, since it can parallelize the PoW.
In a completely non-parallelizable PoW (as FreeTrade pointed out recently and I just commented on), the fastest single processor takes over the system - but we have a perfect protection against a botnet take-over (because parallelization does not help).
In the concept I am thinking of right now, we should be able to combine the advantages of both worlds, depending on how we build the PoW (described in a bit more detail in my recent reply to FreeTrade).