I would definitely rather see roads like this in DCR's hands than MassDOT's, and while the City of Boston would certainly do a better job with this redesign, there's only a handful of municipalities I can confidently say that about. DCR, at the very least, is willing to reduce roadway capacity. We've seen this on Hammond Pond Parkway and the proposed improvements to Memorial Drive. I doubt MassDOT would have come to the same conclusions.
Ultimately, the fact that DCR's mission is for recreational and active uses, as opposed to traffic management, is a great reason to keep any roadway that should have fewer arterial/highway characteristics out of MassDOT's hands. DCR's actions are often not those of an agency committed to safe, active transportation, but that is clearly a main priority for much of the roadway work they do. And in the meetings I've been to, DCR officials always seem to want to provide safer designs, but feel constrained by the "need" to not not cause traffic bottlenecks. This is a far cry from how I've seen MassDOT handle similar projects, and while that is the case, I'd rather see DCR make attempts for more bike and ped friendly roads than MassDOT engage in more congestion relief programs.