Each business has a way of operation and the priority inbox or inbox with all conversations may change according to the needs of different businesses. The best option could be identified after trying out both approaches to handling the conversations.
Here are some tips to think about what may work well for you:
Priority Inbox helps when you have large volumes of real-time conversations and both team members and supervisors want to keep an active tab on how quickly they are responding to customers.
Businesses with low volumes of conversations (each team member handling less than 40 conversations in a day) and those with low concurrency of ongoing conversations may not need to use the priority inbox mode - though the supervisors may still want to use this mode to keep an eye out for the bad experience on the customer side.