I think specifying the requirements for a modern bomber is made difficult by the variety of ground attack missions a "bomber" might fulfill.
The requirements of "high munition capacity, a large combat radius, and long loiter times" closely fit the description of a close air support role, which has been the primary role for bombers and strike aircraft in recent years (Iraq and Afghanistan).
With that said, there are certainly other roles for bombers; missions where strategic facilities, supply lines, and bases/defenses must be destroyed. These are rooted in more conventional warfare than we've seen recently, but I'm less than convinced that they would be rare in a major conflict.
These conventional missions demand speed and stealth not only to penetrate evade enemy air defenses, but also to keep up with intelligence on mobile/time-sensitive targets. This timely delivery problem is hard to accomplish with small numbers of loitering aircraft or where the target has advance warning.
Also, given the proliferation of advanced mobile SAM and radar systems, I'm unsure of the assumption that US aircraft will have clear skies in a future conflict. Certainly in the early days of any conflict this will be untrue, and those are the days where strategic bombing will be most valuable; disrupted enemy infrastructure allow ground forces to move without resistance.
Thus, I think there's a need for both roles--CAS and penetrating bomber--and it seems to me that the USAF is actually tackling these separately, efficiently. While the Reaper lacks a large payload, it seems that the large numbers providing spatial coverage will have sufficient munitions in aggregate. The B-2 was designed to be the penetrator.