Why doesn't the GOP reach out to black voters?
Short, inflammatory answer: Because it's fucking racist, bro.
Longer, nuanced answer (gonna rehash a bunch of Nixonland-y stuff you're already aware of): There are a lot of white voters who, to varying degrees and in various ways, are culturally averse/suspicious/unsympathetic toward black people and who don't want to see politicians and government beholden to black interests. They've been welcome in the GOP and have had lots of their attitudes (about food stamps/welfare, the Civil War, busing, affirmative action, multiculturalism, etc.) adopted by mainstream US conservatism.
Rhetoric that makes black people feel unwelcome in the GOP tells those white voters "We're on your side, against them." Everyone calls that stuff dog whistles, but it's a bad metaphor. A dog whistle can only be comprehended by the dog, but everyone can hear the racial undertones when Rush Limbaugh talks. It's just kept nice enough that it's deniable. Cause they're not worried about offending black people (whose votes they've forsaken), they're worried about offending white people who don't want to be seen as blatantly, explicitly racist.
So pissing off black voters has been a feature, rather than a bug. Even if changing demographics mean that incentive doesn't work for the GOP at large any more, it probably does work for the individual politicians, who are trying to win primaries or get a better standing within conservative circles. Bush may have spoke to the Urban League when he was secure as the president and his party's leader, but when he was in a primary fight, he made that speech at Bob Jones University while they still had a ban on interracial dating.
So really, just basic identity politics. Can't be too nice to Ethnic Group A when shunning them is what gets you the support of Ethnic Group B.
"But their policies should benefit both groups, or at least they should believe that, so why leave votes on the table rather than broaden their base?" Cause even if Bush or a couple earnest policy advisors in the GOP really believe that their brand of pro-business policies would be good for poor black communities, their base supports those policies because they believe they will hurt poor black communities, or at least force the lazy and undeserving to carry their fair share.
Like I said, I don't think this is really new to you. But I noticed a certain tendency among libertarians to be a bit hyper-literal and -logical in looking at things, and even when you think you've made allowances for the shenanigans of humanity... nope! The answer here is just people being dumb and tribal and cruel to each other.
Re: Strategic voting among blacks/libertarians. I think the dilemma for libertarians is more like that of American leftists back in the day (like actual commies). Libertarians don't really have a cultural identity or social institutions outside of politics, and besides being fewer they're not geographically concentrated in the same way. For that matter, your goals affect how you organize. If you're a group that's been historically marginalized, then you're going to want access and power. From the outside it may seem like getting black people elected is a shallow/unproductive goal, but for a group that's been shut out for so long?
I don't like one party systems either, but I don't know how much of that's my own bias. Surely there are tons of counties that are deep blue or deep red without serious issues of cronyism, and even in DC campaigns for mayor and council spots are pretty hotly contested, just with the action happening more in the primaries than the general, so there's definitely a big representative aspect. It's not a good sign that voters cleave on racial lines, but I think the split in party identification is much more a symptom of broading racial issues than the cause.
edit: Why isn't ending the drug war a high priority? Its only constituencies are drug users and a subset of urban policy wonks. That's not a formula for an organized and powerful lobby. Potentially sympathetic politicians are going to see a lot more downside than upside in taking it on.
