A good interactive router (like Altium's) is way more productive than auto-routing. If you don't believe me, watch a YouTube video of someone hand-routing a board in Altium.
I've only found auto-routing productive if you have a TON of low-speed, low-power signals that you need to run between things, and you don't really have any space constraints. In any other designs, you spend so much time configuring the auto-router, that it's just faster to hand-route.
If you're doing open-source designs (even if they're commercial), you should strongly consider giving Altium's new CircuitMaker software a try. It's absolutely free (even for commercial work), and has about 90% of the features of the full version of Altium Designer. The only "catch" is that all of your CircuitMaker projects are accessible by the CircuitMaker community. Like most professional CAD/CAM software, it's also Windows-only.