I like your thinking but I'm not sure the harvest numbers support your notion. Ohio has regulations almost exactly as you describe. Gun season is shotgun or straight walled rifle, lasts only one week, and doesn't open until Monday following Thanksgiving. ML season is a meager 3 days and doesn't open until January. Bow season open first of October & runs into February. In terms of bow hunting for big antlers it's hard to beat Ohio's regulations .... on paper at a glance. But when you begin digging into harvest stats there's an unexpected surprise. Although Ohio has fewer deer than TN, in 2022 they killed 210K deer. TN with it's liberal limits and regulations only killed 165K.
OH's herd is estimated at 700K strong. TN's is estimated 900K. Yet OH is taking more deer from a smaller herd, with MUCH more restrictive regulations. I understand your thought process that shorter firearms seasons, especially during rut would be a rational way to increase buck size. But that's not what actually happens. I'm not exactly sure how to interpret the numbers so I don't. This is a point where I trust the state wildlife agencies to make the most informed decisions they can for their respective state. They catch a lot of he!! and some well deserved, but overall their bottom line objective is to manage the resources for the a hunt that best fits the constituency as a whole. Each state does it differently because the hunting culture and biological factors in each state are different.