The 7BE has been in production since 2014. The wing is hte same, more or less, so re-engining is perfectly possible, however, with the life expectancy of most CFM engines being very good, the real question is will the number of -NGs going to the boneyard provide enough to keep the new build NGs in the air for the next 30 years. Probably more than likely.
The reason for the single supplier is cost saving for Boeing. One thing that really blows costs out of proportion, is too many options and choices. Airbus must be rueing the day they gave in on that with the A380....