For the full voltage range and current as stated, you need to dissipate up to 848W.
That's a big heatsink, and at least several large transistors, probably a dozen modest sized ones.
The specs are absolutely achievable by SMPS alone -- no need for pre/post reg.
For simplicity, I might opt for a hybrid design, iron transformer + rect into buck regulator; LM25119 and similar parts would be a reasonable choice. Power factor is a concern, especially at these power levels (13.8V 40A is 552W; at 90% overall efficiency, 0.5 PF and 120V input, that's 10.2A RMS already!), and I mean just in practical terms. Using a proper offline SMPS is highly attractive.
As it happens, I have a stock design (mains to 24V 30A, LLC resonant) I could apply to such a purpose, or buy a unit ready made. It tends to be a bit noisy in the audible spectrum (would not meet the ripple requirement, unless maybe the requirement is low frequency only) so the buck stage would still be necessary, rather than designing it for 13.8V exactly in the first place.
I do wonder just how sensitive the load is, if it really needs to be 13.8(00..) V and low ripple, or if anything from 12 to 15V would do, and what the effect actually is. I.e. are you asking for precision out of an abundance of caution, or is there a real and present need for it? Compare class A/B to C/D (maybe E) amplifiers for example; SSB vs. FM/PM use, perhaps. Linear amps generally should have better PSRR, give or take biasing anyway, and it may be less effort to fix the latter than to regulate and filter the former.
Even with an SMPS + postreg architecture, the required voltage drop is much smaller than for raw rectifier output. Even if you have a tap changer or variac to compensate for mains fluctuation, the peak-to-peak ripple is still enough to need a hundred watts or so of dissipation with the rectifier. Very low overhead can be used with an SMPS, but mind that loop gain will be lower, and compensation more difficult, as the transistor's operated near or in [voltage] saturation.
Tim