I like mine, which has both tubed and SS output. I think it optimizes some of the earlier and (IMO) harsher recordings on CD, but recognize this thing also has adjustable upsampling from 44.1 KHz to 768 KHz, so it's easier to fine tune if you get ahold of a poorer CD. I use the tube output almost exclusively. It is a good match for my tubed integrated amp.
With a tubed CDP, you have to be willing to pop for $100+ at the drop of a hat when a tube goes. I can switch mine over to SS while the tubes ship, but most do not have that capability.
The other thing to consider is what you listen to and what you're matching it with. I would be more likley to recommend a tubed CDP when it is paired with all tubed components downstream, or with a tubed preamp/SS amp combination.
Finally, it is not a panacea. It will not take your vintage recordings that were put on CD in the early 80's and sound harsh and make them all sound like HQ vinyl. Mine from that era are hit and miss with my deck. Some sound terrific and some are still somewhat harsh (early CDs still were boosted in the midband frequencies as with the LPs, and when paired with CD's perfectly flat response, yielded a harsh sounding disc). Many of the early discs have been remastered, so that solves some of the issue. Still, I believe vinyl is often a much better bet with many pre-1985 recordings, tubes or no tubes.
I wouldn't say it's about taking the "edge off" as such, although as Neil points out it may make some poor digital recordings sound more acceptable. The potential benefits I suppose are really the same as in any tube implimentation, if that's your thing. And of course the ability to tailor/tweek the sound by tube rolling. It's not an absolute good, it's just an option if you're into tubes.
I'll be able to give you a first hand account of the Minimax in a few days, and compare it to the dac I have now, and my NAD cdp.