The only places I have found silos to be useful:
Factory planets - I can't quite seem to balance the P2 and P3 processors perfectly, so I end up either with more P2 than I can convert to P3, or not enough P2 to keep my P3 processors fed. In these cases, I have started to put in a silo with the wee bit of grid I have left. The silo can act as a buffer between the P2 and P3 and allow me to over produce P2. Normally, I route everything back to a launchpad, but this is easier on the link load and does not overload the launchpads (which start out full to the gills and take the finished P3 anyway).

Alternatively, and probably more efficiently, I have installed a silo before the P2s to allow more on-planet storage. If I am out of system, I can reload my process from on-planet reserves, something I can't do from my COs. This requires some manual transferring but adds about 60% more time before I have to visit the system to import/export from the POCOs

This also works for some of my extraction planets, which make P1 only. I have 2x ECUs with 5-6 heads each, a Launchpad, and processors (5 maybe? I forget). In any case, the launchpad can just barely handle the full influx of P0 for the full program run (4 days), but only if the P1 material does not clutter up the launchpad. If I do send the P1 to the launchpad, I start losing P0. Adding more heads just exacerbates the problem, as does adding another processor. After about 36-48 hours, I am over the hump, but I lose some P0 due to dual feed material/product storage overload. I used to handle this by uploading P1 to the CO after 12 hours and 24 hours, but this is a PITA and not possible anyway if you leave system. The use of the silo to hold P0 has eliminated this problem entirely for me.

TL;DR - Silos can be used to solve short-term balancing issues on factory or extraction planets, when and if additional processors do not solve the problem.