For most wildlife agencies the number of "recreation days" provided for and used by bowhunters is important. This is especially true east of Colorado/WY,MT,NM, etc.
Bowhunting wasn't legalized or expanded to "manage" a big game herd. These seasons were created because of demand for recreational opportunity.
Some might think that an agency could increase its deer harvest (again in the east) by reducing bow season in favor of longer firearms seasons. In fact, in states like SC, AL, GA, and others the agencies have found diminishing returns with making firearms season too long. If a firearms season is too long the "urgency" to get out and hunt is less and some just "forget" or neglect to go.
Interestingly, the bowhunter has become more effective since the 1960's and earlier. In the 60's success rates were less than 5% in most states. These days (more deer biggest reason)success rates are 2-5 times higher.
The bowhunter (again in the east) is one of the most avid Doe-takers and can also hunt in urban/suburban areas. So, the bowhunter is more a manager today than 50+ years ago when our seasons were born.
Another thing we all need to remember, especially wildlife agencies, most bowhunters participate in firearms seasons as well. In fact, the number of bowhunt-only archers is less than 10%. Therefore we are often the most avid supporters and users of wildlife management programs. I had to remind my Commission of this every time a "bowhunter" made a jerk-like statement at a public meeting.