I think the answer goes into the following direction:

Peak level based digital leveling is much more precise than the rather sluggish VU meters that required a leveling reserve. According to Sengpiel: "Analog meter (ppm): attack time 10 to 300 ms − reading rms values. Digital meter: attack time < 1 ms − reading peak values. That is really some difference.". Additional remark from me: in this case, of course, you need quite high leveling reserves in order to get even transient-rich material output recorded without distortion.

As Sengpiel notes, you don't need a headroom like in the analog world, you just have to be careful not to go above 0dBFS.
The leveling to a peak level of -6 dBFS was most likely defined by RME out of certain safety considerations, to have a certain safety distance to 0dBFS, because even a leveling to peak level may have a very small inertia, but on the other hand, not to give away too much SNR/dynamic range of the recorded signal.
This is also why you have different reference levels to perform the A/D (and also D/A) conversion with optimum SNR/dynamic.

Additional remark from me:
- Perhaps there is also some idea behind it that A/D-D/A converters might have their sweet spot there.
- It's also practical that for multitrack recordings and later mixing, the sum of the channels in the stereo sum should not exceed 0dBFS too quickly.

Some useful quotes from this Sengpiel page:

http://www.sengpielaudio.com/calculator-db-volt.htm
http://www.sengpielaudio.com/Rechner-db-volt.htm

"Comparison dBFS and dBu: There is no fixed standard, such as -20 dBFS = +4 dBu = 0 dBVU.
The digital peak value scale does not match the analog RMS scale. These are two different worlds"

"There is no such standardized reference. x dBFS is a digital voltage level (peak) and y dBVU or dBu is an analog voltage level (RMS). Digital and analogue are two totally different realms."

"That's why there is no relation between dBFS and dBVU or dBu, whatsoever. Analog meter (ppm): attack time 10 to 300 ms − reading rms values. Digital meter: attack time < 1 ms − reading peak values. That is really some difference."

"Advice: Watch only your digital meters and go up to 0 dBFS, but never go over this mark. We use "headroom" in the analog domain. That is OK, but we don't need digital "headroom" as an always "unused" forbidden zone. You are free to choose your private headroom, if you like that, but there is no standard that you have to do that. The demand for a high modulation level, stand in the contrary to the claim, to avoid overloading."

"The EBU broadcasters have a problem, because they want to use the old slow meters with the dBu scale (attack 10 ms, quasi-peak) of the analog times for digital recordings. The rest of the world looks always at the fast digital meters (attack < 1 ms, peak) with the dBFS scale. Forget looking at the dBu scale of the meters."