The peak current would be inversely proportional to the inductance, so unless one needs 10A DC output, for 3-5A DC and 2mH 20A peak should be enough. Besides that we are not dealing with DC current, 20-30A would be the peak of few ms pulses...
Yes, I took the worst case figures given. You certainly don't want it saturating around the peak, that would cause the current to increase suddenly.
Anyway considering the energy of the load, e.g. 20V*3A*10ms = 0.6J, we are in that order of magnitude. 
Yes, that implies we are somewhere around continuous current mode.
You might use even more then, to get more stable output voltage with respect to load current; or use less, so it's closer to a peak voltage switch thingy (that is, the output voltage is about equal to the peak voltage at the moment the switch turns on), with an inductor to help absorb the peak current surges (which would then be higher, maybe say 40A or something, but not unlimited destructive peaks; of course, at the expense of even worse power factor).
What changes is how much capacitance you need for filtering, and the response rate of the control loop (gain and cutoff frequency).
Incidentally, filter capacitance tends to rise with inductance, because the impedance of the filter Zo = sqrt(L/C) you don't want too high -- this is equivalent to the output impedance at its resonant frequency, when the resonance is critically damped. In other words, a step load change will see a peak voltage change of about Zo * delta I. In still other words: suppose the load suddenly stops drawing current, so the inductor was charged to some energy (say it's over 1J in this high-L case), and the load stops so that energy is discharged into the filter cap, so its voltage overshoots by that amount of energy.
So, to put numbers to that, we can use an energy argument, and say the capacitor's voltage was 10V, and its value 20mF (just guesses). Its initial energy was E = 0.5 C V^2, or 1J also. Say we add 1J to it. Oh good, that's an easy ratio, it's doubled so it's obvious V has sqrt(2)'d, or 14.1V. A 40% overshoot is pretty generous, and probably not desirable, so you'd probably want a lot more capacitance.
For the general case, invert the equation: Vfinal = sqrt(Etotal * 2 / C). If you continue substituting intermediate formulas until you get back to just the intial voltage and current, and inductance and capacitance, you'll have proven the same peak voltage change as calculated by Zo.
This implies a smaller L is desirable, which is more or less true, until modulator nonlinearity causes instability, or PF gets so bad it's just a mess.
In short, a middling value, where the inductor current goes nearly to zero every (half)cycle, at full load, is probably not horrible.
The same mechanics apply to SMPS design -- you don't want to use too big of an inductor relative to the filter capacitors, or if you have to (usually because inductor losses are just too high to run at high ripple), you need to use more caps to keep the output impedance sensible. That's the gist of most ATX PSUs, and why they responded so damn slowly (cutoff frequency of just a few kHz!).
BTW I already know about those inductor saturation tester projects and the advantages of a real switching PSU, but was just wondering about the feasibility of this different solution.
It's absolutely feasible, a whole generation of "brick shithouse" boat anchors were designed this way! But there's really only one reason why they were: they had to use SCRs to get the reliability and efficiency up, and the huge pile of iron is basically cleanup for that.
Once good-enough transistors came along -- even just mere BJTs -- these designs were quickly migrated to more economical, and better performing, ones!
Which, on a related note, generated more than a few tales of caution: the original RCA 2N3055 was a diffused mesa process or something like that I think -- almost as slow as a germanium power transistor, fT in the 10s kHz. Laughably useless for these sorts of things. When Motorola offered their epitaxial version (with fT ~ 2MHz, but they can't put that on the spec sheet because 2N3055 is a JEDEC spec -- not a description of the part you've ordered!), it was capable of switching comfortably in the ultrasonic range. Until a process change occurred, or someone in purchasing bought the wrong brand, or old stock or something, and KABOOM, product failures left and right... Fortunately, we don't have to worry about this much today (but it does remain a good reason to avoid overly general part numbers like those).
Anyway, the phase controller -- it's still a neat design exercise, especially if you run across an occasion that really is
perfectly suited to phase control, or SCRs (or TRIACs) -- these are ever-fewer, but luck favors the prepared, as they say. But beyond a design exercise, actually building it -- if you learn better through doing, yeah, go ahead and do it.
Here's a tangentially similar project I once did,
Schematic:
https://www.seventransistorlabs.com/Images/SCR_Inverter.pngOverview:
https://www.seventransistorlabs.com/Images/SCR_Inv1.jpgUnloaded, low frequency waveform:
https://www.seventransistorlabs.com/Images/SCR_Inv2.jpgLoaded, showing... commutation current I think? as well as supply voltage (fat trace is 120Hz supply ripple):
https://www.seventransistorlabs.com/Images/SCR_Inv3.jpgZoom on commutation event, it's mostly smooth but notice the very slight, but very sharp, kinks at turn-on and snubber diode recovery:
https://www.seventransistorlabs.com/Images/SCR_Inv4.jpgThose tiny (fractional volt) but fast (sub-microsecond edge) events are what you need to filter, to get a low noise output from an SCR inverter circuit. That can be difficult, too.
And also, of course -- all of this notwithstanding the Agilent mentioned above. It's not clear to me that that's being used the same way. Similar applications include passive power factor correction (which you also see in later ATX PSUs from time to time, before active PFC and 80 Plus took over). But whatever it's doing, clearly that's how they chose to do it!
Cheers,
Tim
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