The Axis recoil lug is not an impediment to accuracy across a wide range of shooting styles. Maybe benchresters will see a difference, but for the vast majority of shooters, the difference will not be noticeable. I suspect the only reason it hasn't been done before (or at least hasn't been done as prolifically) is the recoil lug being part of the barreled action had become the paradigm for bolt actions. Even that paradigm probably started with the recoil lug on the receiver until it was shifted by major designs like the Savage 110 and Remington 700. I'd like to think the Axis recoil lug was only possible thanks to modern plastic manufacturing, but it's possible Savage would've gone with the design regardless of what stock material was cheapest.

My take on custom Axises: They are fine rifles to build on with a few caveats, many of which have already been mentioned. You will have fewer choices for parts, but the parts that are shared with 110s still give you a number of options. The receiver is always a long action with a closed top, which means it will have extra weight if you're not trying to build a heavy gun. Also, some of the options out there if you're interested in using AICS magazines (chassis systems, CDI bottom metal) are only geared toward short action magazines.