Additional merits to Wetterich's "Universe without expansion" compared to standard cosmological redshift interpretation? A recent news item in Nature promotes Wetterich's preprint "A Universe without expansion". All sounds very exciting but hard to judge for non-experts.
As I understand from the Nature's article, the Wetterich's approach would be consistent with  $\Lambda$CDM, thus providing a radical re-interpretation of known observational facts. 
I've got particularly intriguing the following statement from the preprint's introduction: "Furthermore, an important feature is the simplicity of our model covering both inﬂation and present dark energy, dominated by the same simple quadratic potential."
Is it true that Wetterich's growing mass interpretation of cosmological parameters contains fewer assumptions than the usual (as far as I understand, separate) treatment of cosmic inflation versus radiation-, then matter-dominated epochs?
And more generally -- are there additional merits of this unconventional approach to make it preferable over the present "redshift=expansion" dogma?
 A: I've quickly glanced over the paper, and my basic impression is the same as a lot of what you see in the Nature article:

The idea may be plausible, but it comes with a big problem: it can't be tested. [...]  "I remain to be convinced about the advantage, or novelty, of this picture," says Niayesh Afshordi, an astrophysicist at the Perimeter Institute in Waterloo, Canada. According to Afshordi, cosmologists envisage the Universe as expanding only because it is the most convenient interpretation of galaxies' redshift.

When you read the paper, at first it looks as though it is a testable theory and not equivalent to ΛCDM. It has no singularity at the big bang, which seems like it would clearly make it a different cosmology. But near the end of the paper, he shows that you can do a change of variables, affecting the metric $g\rightarrow g'$, not the coordinates, such that in the new variables, there is a singularity (and masses are constant). He calls the description in the new variables the "Einstein frame," and says it's the one to use if you want to compare with observations. So AFAICT this description is simply the standard one that has been subjected to an unobservable change of variables.

Is it true that Wetterich's growing mass interpretation of cosmological parameters contains fewer assumptions than the usual (as far as I understand, separate) treatment of cosmic inflation versus radiation-, then matter-dominated epochs?

No, it can't have a different number of assumptions than the standard theory, since it is the standard theory, just subjected to a change of variables. Inflation has a lot of unsolved problems, and these problems can't be solved by making an unobservable change of variables. 

And more generally -- are there additional merits of this unconventional approach to make it preferable over the present "redshift=expansion" dogma?

"Dogma" is not the appropriate word here. There are extremely strong reasons, including detailed evidence from laboratory experiments, for interpreting redshifts as an increase in the ratio of cosmological distances to atomic scales such as the Bohr radius. The question of whether it's the cosmological distances that are changing or the atomic scales is one that GR has never pretended to answer. This has been clearly understood ever since Einstein first published his theory in 1914, and if you read the 1914 paper, you'll see that Einstein is very careful to explain that measurements are all relative to some meter-stick. In Wetterich's picture, the meter-sticks are simply shrinking.
