Saved searches are scheduled across the whole search head cluster. (with some additional conditions like a cluster member being in detention). That's what search head is for. Also - limiting searches to just one SH would inevitably lead to delayed/skipped searches. It won't solve the performance issue.
Even if you have multiple indexers holding the same bucket, the indexers holding primary copies respond with results from those primaries - it's by design and lets you distribute the search. Even if you had a possibility to get results from just one indexer, there would be no guarantee that you'd get all events from given time range because with sf=rf=3 and 4 indexers you'd still probably hit (actually would _not_ hit) some buckets which are not present at that chosen indexer.
So your idea is not a very good one.
You can use site affinity to force search heads to use only one site. But again - especially if you already have performance problems - that's counterproductive.
And from experience - it's often not the _number_ of searches but _how_ they're written.
