Yes, what Harveyslake said. The science courses for nursing are not the equivalent of "for majors" science courses. I've taken both and they are night and day. I thinks it is very unlikely BSNs will ever take over the lab.
In California, regardless of your actual degree, you can be a CLS so long as you meet all the requirements. The allied health science courses that nurses take do not count. However, BSNs that did take the "real" classes would be in a position to meet requirements although given the number of units for all those classes the time to complete the necessary education would be extended considerably.
Bachelor's degree (baccalaureate) with specific course requirements:
16 semester or equivalent quarter units of chemistry, which must include clinical chemistry OR analytical and biochemistry.
18 semester or equivalent quarter units of biology, which must include hematology, immunology, and medical microbiology.
3 semester or equivalent quarter units of physics (light and electricity
Training or experience
Minimum one year of post-baccalaureate training
Minimum one year of work experience.
Training or work experience must be comprehensive to cover all areas of the clinical laboratory.
Training or work experience must be in a clinical laboratory.
ExaminationsThe following certifying organizations are approved by the Department for the CLS generalist licensure examination:
ASCPi (international) certification
There are also specialties within medical lab science:
Clinical Chemist Scientist License
Clinical Cytogeneticist Scientist License
Clinical Genetic Molecular Biologist Scientist License
Clinical Hematologist Scientist License
Clinical Histocompatibility Scientist License
Clinical Immunohematologist Scientist License
Clinical Microbiologist Scientist License
Clinical Toxicologist Scientist License
Also, CLS/MLS and MLT are not equivalent. Medical Laboratory Scientists have a bachelor's degree. Medical Laboratory Technicians have an associate's degree or technical certificate. Some institutions and/or states limit the type of testing MLTs can perform. Generally, an MLS performs more highly complex testing requiring interpretations and correlation of data, as well as more intense trouble-shooting processes. (http://thepathologycenter.org/MLS-Program/faq/)