why perform a query involving
$group which in principle processes each document sequentially
This is not necessarily true. The database engine is designed to be optimized for such type of operations, when you architect your database properly. Parallelism and set-based operations of database engines are not the same as sequential processing.
The more information you provide it, i.e. a complete query, and reliant you are on database operations to be handled in the database layer, the more efficient it can potentially be in processing and serving the results. The engine comes up with a plan to execute in the most optimal way it believes, based on all of the information it has at hand.
Wouldn't the 100 simultaneous, separate query be faster?
Generally, no, because of what I said above. There is also overhead for those 100 simultaneous queries, both from a concurrency standpoint and from hardware bottlenecks such as returning more data across the network than if you only returned the final processed result set from a single query.
Then you'd also end up re-assembling those 100 queries results and doing your aggregations in the application layer which typically is less performant than letting an optimized database engine do that work for you in the most efficient way it knows.