I wonder if those are actually what the OP is talking about, because they function differently. These examples–of what we call “do-support”–serve the purpose of subject-verb inversion. (It’s also called “do-support” when it’s done for negation.)
I think the OP in particular is more concerned with this “pointless modifier.” The above mentioned wiki article describes some of the other functions of do, such as in elliptical clauses, where it’s functional utility is manifest:
I don’t like fish, but my wife does.
My brother didn’t finish high school, and neither did I.
You don’t really want to go, do you.
Of course, it isn’t only do that serves this purpose – it’s auxiliaries in general. English is just “forced” to use do when there otherwise isn’t an auxiliary.
I can’t eat fish, but my wife can.
My brother won’t finish high school, and neither will I.
You shouldn’t really go, should you.
Literally, dwi’n siarad Cymraeg is a contraction of yd wyf fi yn siarad Cymraeg, which (word by word) is «particle» am I «particle» speaking Welsh. So yes, it’s a periphrastic, but no, it’s not “do.” You can use “do” in that sense in the spoken language, but the basic construction relies on bod “to be,” not gwneud, “to do.”
“I spoke Welsh” could be:
siaradais i Gymraeg (word-by-word, spoke I Welsh) dw i wedi siarad Cymraeg (word-by-word, am I after speaking Welsh)
or nes i siarad Cymraeg (word-by-word, did I speaking Welsh)
The last two have some variation: these are South Welsh colloquial forms.