That probably won't work. Blue would have an incentive to prove red failed, so if red initiated a big long term project (say, building a new high speed rail network, or a new dam, or incentives to build auto factories or whatever that cannot be done in the every X years switches happen), blue will do their best to sabotage it. This happens in politics already (e.g. public transit projects started by previous governments get sabotaged), let alone if there's an adversarial relationship by the people supposed to be directly directing and overseeing this stuff.
Hmm. I guess the “public transit projects of previous governments being sabotaged” is by design. Regardless of two-party politics, if the people vote into power a new representative who disagrees with the previous one, then they’ll kill those projects. And they’ll spend their time campaigning on the basis of that. This results in “slow government” which – at least IMO – is a Very Good Thing.
But for agencies, you want the opposite – you want fast reaction to changing environment. So in that sense, career bureaucrats are an advantage as long as they remain relatively politically independent and prioritize based on requirements more than perception. The problems arise when they become affixed to one of the parties, but without the checks and balances.
I think this is maybe okay as long as the “fast reaction” has a “fast undo.” Otherwise a new executive (and their predecessor) actually has less power than the agencies within the executive branch.