It was actually the bad old AFL that refused to create unified unions for new industries and instead parcelled out parts of them to old unions. The innovation of the CIO was to charter new unions for each industry.
Unfortunately, that tradition has died and I'm not sure that a new union has been chartered by the AFL-CIO in decades, maybe since the merger back in the mid-50s. Health care is a classic example where instead of chartering a new union, it's ended up being colonized by a whole mess of competing older unions.
There has been some attempts recently to have the AFL-CIO at least referee inter-union competition and grant franchises to certain unions for organizing sectors in various locations, but it hasn't been completely effective. And the Carpenters left the AFL-CIO partly because they wanted to avoid the referee fights and have a free hand to organize where they wanted to.
-- Nathan Newman