When I here someone misuse this phrase I assume they are just ignorant and I automatically disregard everything they say. It’s right up there with the misuse of the phrase “It begs the question …”
As part of colloquial English quote/unquote is fine. Attempts to change it to the pedantic quote/endquote are silly and useless because pedanticism is the opposite of colloquial.
Back in the 70’s (give or take a decade) it was fairly popular where I worked for anything that was ersatz, phony, of questionable origin, or otherwise suspicious was a quote-whatever. Never was an end-quote or un-quote needed because it was a one-word or short phrase that was being “quoted.”
His quote-lunch was made up of quote-meat and quote-vegetables. A common way of putting things.
Whenever someone is actually trying to repeat as closely as they can some other verbatim statement, I’m siding with UncleRojelio unless I knew beforehand the speaker was poorly educated and actually had something meaningful to say, however poorly.
I am tempted to react the same way when people use ‘here’ to mean ‘hear.’ But of course, I tell myself that it’s not really a good way to live my life… you know, finding ways to dismiss people based on pedantry.