I'm going to possibly ruffle some feather here... finding a new job is great and all, and likely a somewhat easier way to get promoted, more money etc. I can't imagine sticking around in one place for 10 years, so I can totally get behind the idea of looking outside the company.
With that said... I wouldn't leave these conversations the same way you have, OP. I'd ask for the opportunity to get more work (as you have done), and if told that a plan would be developed, I would ask how soon to check back in. If not given anything firm, I'd give it a month or two, max, before bringing it up again. If my present boss isn't too keen on executing that plan, I wouldn't feel too badly about jumping up another level to get the ball moving as well (after talking to my direct boss at least a couple of times).
At the same time, I'd keep my own eyes open for things I could do that are beyond my responsibilities. If someone else is doing higher level work, I ask to work with them while they do that task, and learn from them. Then, next time, I ask if I can take the wheel and give it a go myself. I would also keep an eye out for work that isn't being done by anyone, that can improve efficiency, bring more money in for the company, elevate your team's position in the company, make the boss look good and so on. Both of those things will show much higher initiative than waiting around for someone else to make your future for you. Also, learn on your own time too - I don't know what industry you are in or what you do, but there's always something to learn to better yourself.