Virtually all modern long range ballistic vehicles use a post boost vehicle (PBV, sometimes called the bus) to fine tune the trajectory. Even a small delta between the required velocity and the actual velocity could cause the warhead to miss by miles. I doubt you could get close to the CEP levels of current missiles without this technology, especially with solid propellant missiles.

In the case of MIRVs, the PBV also serves to send each warhead to it's specific target. The PBV is usually liquid fueled with hypergolic propellants due to the need for very fine tuning of the trajectory combined with the need for long term storability. The old Minuteman IIIs use this technology, as do the Trident SLBMs. I'd be willing to bet that the upgraded missiles will also use hypergolic propellants for the bus. The Russians also use this technology for their missiles, even the single warhead SS-25.

I suppose you could use a solid propellant gas generator for the same purpose but it'd probably be harder to get the same level of control. Hybrid propellants could also work so long as they meet the storability requirements.

A MARV warhead could increase accuracy substancially, as was the case with the Pershing II IRBM back in the 1980s. It could also make it harder to intercept the warhead with a terminal defense weapon like the old Sprint ABM. Recently, Russia tested a new ICBM that was said to contain some form of maneuverable warhead, perhaps one powered with scramjet technology. They said such a warhead would defeat missile defenses like what the US is building. Something doesn't add up. A scramjet can only operate in the atmosphere. Most of our current ABM missiles are designed to hit their targets well above the atmosphere, before a scramjet engine could fire. I could see them using a bigger, more powerful PBV to change the trajectory of the warhead by an amount greater than our ABMs could handle, but it'd need to be rocket powered to operate in space.