Ah, interesting, Steve (at least, I think so). And didactic. Ta. Your mention of Merriam-Webster made me reach for my Fowler, as I suspect what Fowler calls MWCDEU (Merriam-Webster's Concise Dictionary of English Usage, 1995) is a little US-centric, possibly a prejudice of mine: Fowler treats it as an important resource. As you pointed out - MWCDEU's disjuncts (Fowler calls them sentence adverbs) are commonplace: actually, basically, usually, although thankfully and hopefully are contentious, perhaps because they differ in their formation, and in aspects of how they resolve grammatically.

Fowler's viewpoint (2013) differs from MWCDEU: in speech, "proceed with gay abandon" (I love Fowler!), but when writing or presenting then consider the audience, as rearguard actions exist against its use, not least by language faddists and by those who are simply irritated by it.

An even more authoritative resource, my missus, who teaches in one of the London University colleges, objects because it sounds ugly and can, on rare occasions, be ambiguous, and then she referred to the urban myth of it being a slapdash translation of the German "hoffentlich". Now, the good professor would not mark students down for using the word in that way, but she suspects that other academics may do so (presumably with a "see me" in red next to a mark out of ten at the bottom of the homework).

So I wouldn't agree (add sentence adverb of your choice here) that the battle is lost, but I wouldn't put money on a victory for the people who don't want it as a disjunct.