Why are Boxes 3, 4, and 5 separate if they're all compatible with Box 1?
Boxes 3, 4, and 5 are separate because they are groupings of different types of brake calipers/types. They are separated for convenience because they are distinctly different from each other:
- Box 3 contains traditional cable-actuated road rim brake calipers, including a few that are designed to mount under the bottom bracket/chainstays.
- Box 4 contains cable-actuated center-pull rim brakes.
- Box 5 contains cable-actuated (mechanical) disc brake calipers.
Box 1 contains a bunch of brake levers/brifters used to control the brake calipers, etc. in boxes 3, 4, and 5.
Box 6 contains "V-Brake" brakes that require a different cable pull ratio than what is offered in boxes 1 and 2. if one used the Box 1 or 2 brake levers with Box 6 brake types (V-Brakes), the pull ratio would provide too much leverage on the brake for the type of brake which could be hazardous to a rider, hence the "No!" indicator.
Chasing this down from the V-Brakes direction back to compatible brake levers, Shimano gives a stern warning regarding the proper "mode" being set for the brake type being used (word-for-word from the Shimano page):
If the mode is not set correctly for the brake type, the leverage will not be correct resulting in either “inadequate or excessive” braking power.
The brake levers in Box 2 match up well with the brakes in Box 7. The diagram shows that the Box 1 brake levers also will work with Box 7 brakes (a footnote on the diagram states "Braking power is slightly less than standard combinations"), however Box 2 levers are not linked to Boxes 3, 4, and 5 brakes. There is a difference in the pull ratio that is tolerable in the Box 1-7 link, but the corollary match up of Box 2-3/4/5 is not desirable.
One would expect that at least the components from the same groupset to work with each other, yet ST-R353 (Box 1) and BR-R353 (Box 6) are supposedly incompatible based on the chart.
That is a good observation, and after looking up both components, I would have to assume that even though they appear to be from the same groupset by the numbering, they actually are not. ST-R353 is part of the Sora groupset family, and the BR-R353 does not appear to be part of the same family. It is a Shimano part numbering decision.
The likely reason that Box 6 is listed here is because someone can incorrectly assume that because of the common numbering, the two components are compatible, when in fact they are not. So Shimano chose to distinctly call out that the ST-R353 is not compatible with BR-R353 (and ST-R460 is not compatible with BR-R463). There are other V-Brake models besides these two. However, these two V-Brake models just have a greater potential for a false assumption of compatibility due to similarity in their numbering with the Box 1 brake levers/brifters.