This is an interesting thread, and a subject that I have been thinking about a lot over the previous year's experience with my EKO 60 and 500 gal of storage (both indoors in the basement). I have a somewhat unusual setup, in that we are heating two houses - one a moderately insulated farmhouse, and the other a 70 ft barn converted to a house, with 11' ceilings and moderate insulation in half of it. I had previously used 3 hot air oil burners ~ 70K output each, to heat it. Overall, it is equivalent to about 3 normal homes, with the barn being twice as large as a regular house, and using about twice the oil of the farm house. I used 11 full cords of wood last season, which sounds like a lot, but in fact is pretty much in line with heating the equivalent of 3 conventional, moderately insulated homes.
I burn 24/7 in all but the warmest shoulder seasons. In my case, the heat storage is only about 100K BTU total (assuming 600 gal total including the boiler, with a 20 deg swing). Those BTU's from storage would only provide heat for a few hours under moderate conditions. Of course, at -20 deg, the boiler is running flat out, and just about keeping up. In most cases, I keep a hot bed of deep coals, and feed the furnace every 4-6 hours, which works out about right to keep a hot, clean fire going. If I maintain the bed of hot coals, it burns extremely clean, and gassifies beautifully whenever it comes on.
So it seems the issue of storage becomes one of the ratio of storage capacity to heat usage. In my case, even if I had 1,000 gal or more of storage, it still wouldn't be suitable to build intermittent fires all the time, as I could get at most perhaps 8 hours from the storage. OTOH, if I were heating only one house, reducing my load by 2/3, then 1,000 gal of storage could actually provide the necessary heat for 24 hours, and would be ideal. So there must be some mathematical ratio of total storage capacity vs. heat load, where using storage with intermittent fires is more advantageous that a more or less continuous burn.
Despite that, the relatively small storage I do have in invaluable, as it provides a kind of "thermal battery", drawing off heat if the fires gets low and before I can get it back up again, or in the coldest weather, providing a buffer. However, adding more storage tanks in my case wouldn't really accomplish too much, as I still could never add enough to be able to run off the storage for more than 12 hours or so.
Of course, the real solution is to reduce the required heat load through better insulation, and radiant heat delivery to utilize cooler water, which in effect is the equivalent of adding more heat storage. Anyway, the storage question is nuanced, and I think just assuming more storage is always the answer is not necessarily correct. It depends on the specifics of the situation.