Ask HN: Startups – how are you using contractors / consultants?

I'm new to consulting and my niche (based on experience and expertise) is on helping startups scale. I find that most meetings I take with startups often turn into a bait-and-switch: they ask me to come in and meet their team after their initial interest, but once I'm in the door, it turns into an interview for full-time. My thoughts are that consultants can be cheaper over the long haul because our engagements can be shorter or turned off/on for exactly when you need me, saving a cash-strapped business (like a startup) money while delivering oversized value. Also, if they're worried about not being invested in the success of the company, I'd love happy, long-term clients, so their success is my success. That's my pitch, but it doesn't seem to be converting. Perhaps my thinking on the applications of where startups use consultants is wrong? How do you use contractors and/or consultants to get your startup work done?