He wasn't hanging out in bars in the mid-70s, despite the "Bukowski drank here" claims you can hear in every bar in Los Angeles (the claims are even worse in San Pedro, where he never set foot in any of the bars, yet everyone seems to have a story of seeing him in a bar, or drinking with him in a bar).
For what it's worth, he never mentioned "The Study" bar in a poem or story (or novel, or...). I understand why you might make the assumption, but I think it may be rather unlikely that he frequented (or visited) The Study.
I also understand why you might mourn some of the torn down spots in Los Angeles, since we have a bad habit of bulldozing and erasing our history here. But I can't imagine that tearing down that generic box in the pictures was necessarily a bad thing.