As someone else said - often it's not possible for you to do much hands on stuff while shadowing. When I shadowed, I was not a paid employee, and thus a liability if I were to get injured on the job.
I finally got hired to work at the clinic after 9 months of shadowing, but it was only because a vet assistant quit unexpectedly and I was already somewhat familiar with the staff and the clinic. I hoped the job offer would've come 6 months earlier, but late is better than never. I think it's often times unrealistic to expect a job to come out of shadowing for a couple weeks. It can happen, but not always. The job market is not great, and if you're in school and can't work full time, it's often not the best economic choice for clinics to hire someone who can only work 20 hours a week.
And finally, as Minnerbelle said, it certainly takes time out of the tech's already busy schedule to show someone how to do laundry, work the autoclave (there are so many different instruments and packs to learn and recognize!), etc. I offered to help with laundry once while I was shadowing, and they just said "no, don't worry about it, you don't work here." As I shadowed for longer, the vet started letting me help out more and more with tiny things (restraining, drawing up vaccines, counting pills, grabbing the kitty scale from the back, etc.), but yeah, I wasn't a paid employee. It is a nicer feeling to actually be productive, but sometimes that isn't possible given the circumstances.