IMO the main drawback is just the downtime: it's not normally acceptable to restart things in between the indexing and searching phases, because people mostly want to search the data as it arrives. Furthermore if you want to do some more indexing then you must restart the node again, breaking any ongoing searches.
It's more usual to have a hot/warm setup, often with ILM to move indices from the hot tier to the warm tier and do various other optimisations like force-merging them at the same time. That way you can scale the hot (indexing) and warm (search) tiers independently and can scale the hot tier down (all the way to zero if needed) when there's no indexing taking place, without affecting the warm tier.