Sometimes when we are promoted to management we try to prove our worth by placing ourselves in the flow of activities to help make fast decisions (taking calls, responding to emails) and be aware of everything. This is one of the reasons someone will get a company cellphone at this time.
Being a part of all of the activities is okay in the short term but trying to work this way long term will be a limiting factor in your development and will wear you out. You should get really good at developing your team and processes and letting others make most decisions for themselves.