Veterinary medicine should be raising the bar in our every day practice. This is accomplished in part by having knowledgable and skilled veterinary technicians provide high quality patient care. Having non-licensed staff perform technical skills lowers the standard of care. You claim there are not enough techs, so let an assistant gain venous access. This is a flawed argument. That is like saying, "There aren't enough veterinarians, so let the veterianary technician perform surgery." They are both physchomotor skills, right?
Pay your veterinary technicians a living wage, treat them with respect, detoxify work environments, and engage their critical thinking skills. Do these things and I think you'll find your "technician problem" will begin to solve itself.