Restoring service fast and finding out why it broke are both necessary — and ITIL 4 deliberately keeps them as two different practices with two different clocks.
On a live outage, the instinct to fix the root cause immediately is strong, and it's exactly the instinct ITIL 4 asks teams to resist. Incident management exists to restore normal service operation as quickly as possible, minimizing business impact — speed is the entire objective, even if the fix is a workaround that doesn't touch the underlying cause. Problem management exists to identify, document, and eliminate the root causes of incidents (and to reduce the likelihood and impact of future ones) — thoroughness is the objective, even if it takes far longer than any single incident could tolerate. Conflating the two either slows down incident response chasing root cause under pressure, or lets recurring root causes go uninvestigated because each recurrence gets treated as "just another incident" to work around again.