Question: is it common for lead software engineers to mostly do paperwork or is that just a quick of my current program?

Where I work it is very common for those titled "software leads" to be almost completely hands off the software. They deal in hiring, fielding user comments and commitments, and scheduling. I would like to be a lead but I was always under the assumption that dev leads had more of a design and/or architect role. Sort of a big picture thing rather than middle management which is what this feels like.