I think part of the stem problem is interest
I agree. But some schools don't appear to inspire any interest, particularly in tech subjects. A few of the school open days we visited were very poor with their "tech" displays, whereas a couple were really good with robotics etc. There's so much more than can be done to inspire kids to want to go down a science/tech route yet the schools themselves often don't do anything to inspire and encourage it.
UCLAN for example have an annual science festival weekend aimed at primary school kids. The place is really buzzing with all kinds of displays, presentations, lectures, hands-on interactive activities etc and it has an amazing level of support and popularity, attendances increasing yearly. It really does inspire the kids with subjects like forensics, medical science, robotics, and has displays from employers such as aerospace, nuclear fuels, etc. The common theme is the desperate shortage of people wanting to work in such industries and, hence UCLAN putting on the annual festival, the shortage of applicants for the courses in those subjects provided by UCLAN. Obviously a long term strategy in the hope of getting the next generation of secondary school pupils to aim for a science/tech career by getting today's primary school kids interested.