diff --git a/pkg/ccl/backupccl/backup_processor.go b/pkg/ccl/backupccl/backup_processor.go
index 591b5a3930a7..35d4cdc5fc86 100644
--- a/pkg/ccl/backupccl/backup_processor.go
+++ b/pkg/ccl/backupccl/backup_processor.go
@@ -217,8 +217,8 @@ func (bp *backupDataProcessor) Next() (rowenc.EncDatumRow, *execinfrapb.Producer
 
 func (bp *backupDataProcessor) close() {
 	bp.cancelAndWaitForWorker()
-	bp.agg.Close()
 	if bp.InternalClose() {
+		bp.agg.Close()
 		bp.memAcc.Close(bp.Ctx())
 	}
 }
diff --git a/pkg/util/bulk/tracing_aggregator.go b/pkg/util/bulk/tracing_aggregator.go
index c5b3aa5c7d94..4fe8eaeaad1c 100644
--- a/pkg/util/bulk/tracing_aggregator.go
+++ b/pkg/util/bulk/tracing_aggregator.go
@@ -35,15 +35,13 @@ type TracingAggregatorEvent interface {
 // A TracingAggregator can be used to aggregate and render AggregatorEvents that
 // are emitted as part of its tracing spans' recording.
 type TracingAggregator struct {
+	// sp is the tracing span managed by the TracingAggregator.
+	sp *tracing.Span
 	mu struct {
 		syncutil.Mutex
 		// aggregatedEvents is a mapping from the tag identifying the
 		// TracingAggregatorEvent to the running aggregate of the TracingAggregatorEvent.
 		aggregatedEvents map[string]TracingAggregatorEvent
-		// sp is the tracing span managed by the TracingAggregator.
-		sp *tracing.Span
-		// closed is set to true if the TracingAggregator has already been closed.
-		closed bool
 	}
 }
 
@@ -62,20 +60,17 @@ func (b *TracingAggregator) Notify(event tracing.Structured) tracing.EventConsum
 	eventTag := bulkEvent.Tag()
 	if _, ok := b.mu.aggregatedEvents[bulkEvent.Tag()]; !ok {
 		b.mu.aggregatedEvents[eventTag] = bulkEvent.Identity()
-		b.mu.sp.SetLazyTagLocked(eventTag, b.mu.aggregatedEvents[eventTag])
+		b.sp.SetLazyTagLocked(eventTag, b.mu.aggregatedEvents[eventTag])
 	}
 	b.mu.aggregatedEvents[eventTag].Combine(bulkEvent)
 	return tracing.EventNotConsumed
 }
 
-// Close is responsible for finishing the Aggregators' tracing span.
+// Close is responsible for finishing the TracingAggregator's tracing span.
+//
+// NOTE: it must be called exactly once.
 func (b *TracingAggregator) Close() {
-	b.mu.Lock()
-	defer b.mu.Unlock()
-	if !b.mu.closed {
-		b.mu.sp.Finish()
-		b.mu.closed = true
-	}
+	b.sp.Finish()
 }
 
 var _ tracing.EventListener = &TracingAggregator{}
@@ -96,7 +91,7 @@ func MakeTracingAggregatorWithSpan(
 	agg.mu.Lock()
 	defer agg.mu.Unlock()
 	agg.mu.aggregatedEvents = make(map[string]TracingAggregatorEvent)
-	agg.mu.sp = aggSpan
+	agg.sp = aggSpan
 
 	return aggCtx, agg
 }