This is the way I understand it. Please feel free to correct any errors, etc:
The B1-A was designed to be a high-level bomber, just like the B-52 was.
But by the time the A model was coming to fruition, the Soviets had developed AA missiles that could knock down high-flying bombers.
The B-52s mission was then changed to low-level, under the radar, penetrations.
IR, etc pods were added under the nose to facilitate that mission, but early model 52's could not handle the stresses of low level flight (much more turbulence near the ground).
Also, by the time Carter cancelled the B1-A program, the Soviets had developed look-down, shoot-down capability on their fighters. (I believe a Soviet pilot's defection to S Korea in a Mig-25 allowed the the US to learn this - much to their surprise.)
When Reagan took over, he changed the direction of our policy towards the Soviets and was determined to force an end to the Cold War. Part of that srategy was based on our highly classified knowledge of the extremely poor state of the Soviet economy. (In my AF job at the time, very early 80's, I was privy to some of that info.)
Reagan was in a hurry to implement his plans, and reviving the B-1 program was a quick and easy way to start off.
But this time, the B-1B was going to be a low-level penetrator from the git go. Or so it would seem. Despite it's capabilities, the B1 airframe, etc, had NOT been designed for low-level penetration from the start.
From all accounts it does a great job of delivering conventional weapons and is the bomber of choice favored by grunts on the ground in Afganistan. The biggest complaints I am aware of are maintenance problems that make it's availability rates very low (much like the C-5) and it's high cost per hour to fly compared to the B-52.
I would maintain the the B1-B served Reagan's purpose admirably and was a key factor in ending the Cold War. It also turned out to be a very capable conventional bomber.
As I said upfront - these are just my uninformed observations and I welcome comments from the real experts on the B1-B.
[This message has been edited by NormanAg (edited 5/4/2013 7:28p).]