You would be surprised what you can put together on a budget with some shopping around. My current tri bike looks like it would have been competitive at the elite level just 10 years ago, yet I'm into this bike for less than $1100 as pictured. I have since changed the saddle and put on a different saddle-mounted bottle cage setup I like better, so add another $100 to that and I'm very comfortable on this bike for several hours. And it's fast too. On flat ground, I can hold a 20-21mph pace for 10+ miles. At least for me, that's a pretty strong pace.
But I agree with you about a dedicated tri bike being faster on a triathlon course than a road bike. Of course, that's what they're designed to do. The important thing, at least for me, is that the tri bike is actually more comfortable going fast than a road bike.