They did, but only as a kind of justification, why nation's mosr expensive and advanced strike assets sit somewhere and do nothing on nuclear alert.
But if you'll see all strategic bomber history, they first obtained nuclear capability, and only afterwards (not always) added conventional one.
Furthermore, typically only part of the force is used, and the least useful one at that.
Say, during Vietnam War older b-52Ds were prefered, despite availability of much newer G/H and mach 2 capable Hustlers.
Same with B-1B, which received even dumbest bombs many years after their introduction, and mostly because of strong push to mske them do something useful during the Gulf War.
Current Soviet/Russian strategic bombers started receiving conventional capability only in this century(!), in form of Kh-555 missile.
But if we're putting conventional bomb truck role to the front, strategic bombers(developing new one, not using already existing ones)are just too expensive for the task. If it's so important, use MPAs, they are sort of large bombers too.