IT infrastructure managers have conflicting responsibilities - fighting fires as they occur, engaging in systematic fire prevention procedures and implementing safeguards. These interruptions erode faith in IT, which is why incidents need to be resolved quickly so that businesses can trust them (and not just an individual) with their IT needs.
Don't risk taking on additional responsibilities while dealing with the crisis. Streamline the process by having technical staff report to their service desk manager, who will then work on it and report back to them after it's handled.
When the senior technical staff work on incidents, they shouldn't create extra work for others because problem management is schedulable. Schedule problem management and reduce unplanned work! Just because a problem hasn't become an incident doesn't that it won’t. Maximize uptime by focusing your resources where needed most.