With 0.1% resistors, there is not much sense in going much beyond 10 Bits. It will still be stable but may not be monotonic. One might get a little better with selected resistors, to get well matching ones for the first few stages. The divider does not scale especially well to higher resolution, as there are quite a lot of relay contacts involved. It's not that bad, but also not especially good. So I don't think it is worth going much beyond something like 16 Bits. As a rough view, I don't see much advantage over a more classical R2R DAC, except that loading to the Ref. source is lower and independent of code.
At high resolution the relays should be bistable types. So they only consume power when switched. This avoids heating of the relays and thus reduces thermal EMF to cause large errors. Normally the relay drivers don't need special cooling. 12 V or similar coil voltage is Ok. A separated supply (e.g. from rectifier on) may be helpful.
Using a ATX or similar computer supply is a bad idea, as this can produce quite some EMI problems. The ref. should not consume a lot a power, so something like a 2x12 V , 5 VA conventional transformer could be all it takes.