I agree that the production has tended to suffer. Even Old Ideas, which had a number of good tracks, was at times held back by production (Anyhow, for example). All of Cohen's songs benefit in a live setting.
Since TNS, it seems to be an artistic choice to use more sparse/electronic production, more than anything to do with practicality or time/costs.
I agree that it has more to do with artistic choice than anything else, but it goes back much further than TNS. Most, if not all, of Leonard's albums (with the possible exception of some tracks here & there) are more sparse than his live performances (he has even said he wanted his first album to be more sparse, but John Simon did not abide by that wish). Songs From A Room, Songs of Love & Hate, Recent Songs, Various Positions, etc. - all pretty sparse. I believe the difference is totally deliberate, & the intention is for a different kind of experience, with the studio albums allowing for a more studied, meditative type of experience, whereas in live performance the intention is for a more upbeat, fiery, excited type of experience. I think it speaks to Leonard's wonderful creativity, that he can perform the same songs in such different ways, at different times & for different purposes, & I cherish both types of experience, & I'm grateful for the opportunity to experience the songs in those different ways. I understand that some people prefer the more upbeat, excited type of experience, but that's a matter of preference. Personally, I love both types of experience, & I don't think anything has suffered, or been held back, by the sparseness of any production.
I definitely agree with the studio recordings being more laid back and sparse than the live recordings… and I actually much prefer his early material the way it was recorded. But as his voice aged, I'm Your Man and The Future in particular, had much more robust instrumentation than what followed.
Don't get me wrong, I don't dislike LC's studio recordings, but to use my example from Old Ideas, "Anyhow" could have benefited from a live drummer, rather than the electronic shaker that was almost identical to what we heard on "Going Home". It is a pretty jazz infused song, and feel it really would have been a stand out track with the drumming to accompany it (some brushes and a few well placed toms).
His earlier albums were sparse, but organically so. That is what I feel is missing on the most recent output. But then again, there are songs like "Amen" that just take my breath away, and that is all programmed, save for the violin.