I can see that with a single 7x7 or larger chest and multiple 3x3 assemblers, but we're talking about the complete opposite situation here. The most important machines, the ones driven by the cube, are all 7x7, and only one can operate at a time. And even the Fabricators are 4x4, so it's impossible to get more than 4 around a 3x3 chest—so the only advantage there is not needing bots to supply it.
As you noted, buffering is very important in Ultracube, although you don't want to go overboard with chest space density for multiple reasons. The former is why I expected a practical increase in storage density with chests that cost much more in terms of research and resources, and felt cheated by a "noob trap" when the investment I made to get them before other important things like robots proved to be wasted. After all, no matter what tricks you can pull off with large chest footprints, their most obvious and primary function is storing things—so why shouldn't the more expensive chests be better at storing things?
You don't have to go overboard with it; I believe a balance can be struck. If you don't want them to offer a better mass storage solution than iron chests, then 60 and120 stacks would make the larger chests just on-par with the iron chests, and I can prove it with math:
Consider the setup of rows of iron chests, with rows of inserters between them: this arrangement is probably the best way to store as many items as possible in minimum space, and is the use-case we want to avoid making the larger chests better at (and thus encouraging the employment of). Now, with many rows of iron chests, the ratio of chests to inserters approaches 1:1, and therefore we can approximate the density as two tiles per chest. Since each iron chest stores 20 stacks, that means the theoretical limit of bulk storage density for iron chests is 10 stacks per tile.
Now, let's consider larger chests in the same configuration of rows of chests linked by rows of inserters. There may be gaps in the rows of inserters, as only one is needed to link two chests, but there is no easy way to make use of that space for more storage. Therefore, if we apply the same process as before of looking at the limit of the ratio of chest-tiles to non-chest-tiles as the number of rows increases, we get 4:2 for 2x2 chests and 9:3 for 3x3 chests, getting a net 6 tiles per 2x2 chest and net 12 tiles per 3x3 chest.
Therefore, if the 2x2 chests could hold 60 stacks, and the 3x3 chests could hold 120 stacks, they would only achieve the same density limit of 10 stacks per tile. Therefore, they would not have greater utility for the bulk-storage situation you wish to discourage.
However, the greater stack size per chest would make the large chests more useful in the use-case you wish to encourage: small buffers of only a few chests. Especially ones that aren't attempting to maximize storage density and therefore are more likely to have access to all four sides of the chest.
Therefore, I contend that raising the stack sizes to 60 and 120 will be a net positive for the mod.