It could be done, but there are a lot of design downsides.
Accumulators 101 (or maybe 301)
Accumulators are mostly used with variable pump, constant pressure systems that need high flow in very small portions of the work cycle. For a consumer log splitter, the cost and complexity kill it. Far cheaper and easier to add engine hp and larger pump.
-Space: Accumulator sizes are overall volume, say '5 gallon'. The amount of oil they discharge relates to the gas charge pressure, initial charge pressure from the pump, and the minimum pressure needed at the end of the discharge part of the cycle. Most of the cylinder extend would be done by the accumulator since it was charged to high pressure. Cylinder would extend quicky under no load, but the internal pressure would rapidly drop down pretty low, then when the cylinder hit the load, the pressure would rise slower because part of pump flow goes to recharge the accumulator as it builds pressure against the load. Because the max and min pressures are so far apart, quite a large accumulator size would be needed even for a small oil discharge volume.
There are ways around this, to use the accumulator for fast advance, then valve it out of the circuit while the pump moves the load at high pressure, then put the accumulator back on pump to recharge during the idle time.
It would work pretty well putting the accumulator on the large volume/low pressure side of the pump, but that would require a two section pump with outside unloading and check valves, not the common (and cheap) two stage pump built into one chunk of cast iron housing.
Not something the average consumer could maintain though.
Just as a gut feel, no calculations, for a system needing maybe 3/4 gallon of supplement, I'd expect at least a 5 gallon size, maybe 7-12 or 10.
-Cost: Accumulator alone will probably exceed $500, plus valving. 3000 psi ones of 5 gallon size are 1/4 inch thick steel shells about like an oxygen torch tank.
-Cycle time may not improve. Depending on when in the cycle the accumulator discharges to help the cylinder, and when it is recharging and robbing flow, the splitting portion of the cycle might not improve, and might even get worse. The overall cycle time probably won't change, but what part of the cycle is fast or slow depends on the circuit design. Extend matters, retract not so much as I am reaching for another piece of wood.
-Time between cycles must be enough to recharge. My typical use is get the wood into the space and start the next extend asap so there may not be time to recharge.
-Increased heat generation and poor energy efficiency. With an open center, fixed gear pump, the pressure varies as needed by the load, so the system is pretty efficient. With an accumulator charged at high pressure, then metered down to low pressure across valving, that energy is concerted to heat. In most systems, that heat is a small part of the work cycle, but in this application a LOT of energy would be going to heat.
-A fixed pump means a fixed cylinder speed and it is easily controlled. With an accumulator, it becomes a constant pressure system and the cylinder speed could vary a LOT based on load. Might come out like a catapult at the beginning of the cycle because the accumulator would have been charged at high pressure. The accumulator would have to be before the control valve, not on the cylinder side of the valve. With a fixed pump, we basically pull the valve lever full stroke and the cylinder moves at a known maximum speed. With accumulator circuit, either we have to carefully feather the lever with each cycle, or add a flow control valve. Both of those options convert energy to heat.
-Complexity. Fixed gear pump and valve and cylinder is about as simple as a hydraulic circuit can get, but how many 'my log splitter don't work' questions show up? Imagine adding accumulator, gas precharge, unloading and sequence valve pressure settings, etc. to the mix of issues.
Notes, comments other than accumulator:
-The flywheel energy storage idea has more potential I think. Still easier to have bigger motor and bigger pump, especially given the number of hours a splitter operates per year.
-Larger rod cylinder only helps in retract direction. Extend speed is the same. Flow out of the closed side on retract must be checked carefully for line sizes, etc.
-Larger rod might allow using regeneration in the extend direction. (Regen won't work in retract.) Smaller rods are way too fast in regeneration. Regen in extend can help speed a lot but ONLY during unloaded portion of the cycle. It does not help the loaded portion when the cylinder hits the load (unless the load pressure is really really low), nor in the retract portion. So, if the unloaded part of the extend cycle is only a few inches, speeding it up a lot won't help the overall time much.
Enough.....kcj