Our bodies are organic tools to the virus. Like anything organic, they're at their best when they're fresh. And, as with any tools, the more degraded they become, the less effectually they perform.
Unlike spirit, flesh is subject to the laws of nature: it decays when left to its own devices, and the bodily machine ceases to function. Once the precious ember of life has been snatched, It knows that time is short. The virus has a narrow window - measurable in days, not weeks - in which to exploit Its instruments of meat and gristle before they fester to pulp.
In this instance, as with all machines, decay is the enemy of control. As each cell weakens and fails, so too do the tracks of nerves vital to domination. Blood sets hard in the veins, sinews draw tight, tissue sloughs off. It must gather fresh bodies while it can, faster than Its present minions deteriorate.
Ironically, time is the enemy of life and undeath alike.
Thus the fictional regularity of uniformly shambling hordes must yield to brutal efficiency; this tide of ruin lurches and crashes forward like a wave cascading over itself, the fastest plummeting forward, the slowest spat out the back. And before you realise, it is breaking at your feet.
The week-long dead can only shamble forward, as best their corrupted flesh will allow. But the freshly dead, with their runny fluids and still-warm cores? If they could sprint you down in life, they probably still can.