Flat trajectory is almost irrelevant in any discussion of the all around hunting rifle. The reason is that most folks shouldn't consider shots beyond 300 yards (present company excepted of course). Additionally, the flattest part of the trajectory is from the muzzle to the zero range. Beyond the zero range the bullet drops quickly by comparison, regardless of the muzzle velocity.
The all around big game rifle might be easier to identify if we consider what it is not. It is not a bench gun. Although it could be used for dangerous game, it is not a dangerous game rifle suitable for close range confrontations. It is not a sniper rifle. It is not a main battle rifle or an assault rifle. It is not a varmint rifle. It is not a small game rifle, at least not with its normal loads.
Although the all around rifle can be viewed in many different ways, the common factors include light weight which allows the rifle to be carried all day without undue fatigue, and it should shoot flat enough and be accurate enough for 300 yard shots on big game. It should have a natural feel and lend itself to shooting from field positions. It should be short enough to be useful in heavy cover. Neither the cost of its ammunition, recoil, or blast should be so intimidating as to discourage regular practice It should be equipped with a sling that can be used as a carry strap or as a shooting aid. The ubiquitous scope sight should be at the low end of the powder scale, and should be small and tough rather than large and fragile. Big game is not normally difficult to see in the open out to 300 yards, so high powered optics serve little purpose. The rifle needs iron sights in case the primary sight is damaged in case there is the opportunity for a shot in very heavy cover, so scope mounts need to be quick detachable.
From these very general parameters, your imagination is the only limiting factor.