What makes a good music radio show? Is it enough to have good music? Or do people prefer a “how about that weather?” “Here’s what I’ve been up to?” Do you want guests? Or is a mixtape enough, provided it’s actually curated by a person as opposed to an algorithm?

I think a really good radio show would be a combination of both excellent music and excellent banter. But if the banter isn't going to be excellent, then I'd say to just focus on making the music excellent. Or at least that was the conclusion I came to when deciding what my show would consist of (I attempted the whole 'talking out loud to myself' thing, but it didn't add any value, so I just went with straight music).

A good radio show like HI54LOFI say, is a combination of both, you need to put good music, but i think you need a good speaker, the banter gonna make the connection with the audience, a bad speaker made a show suck, and just music look like its missing something. Do you think a "just music" show can be relevant?

It depends on the objective of the music show. If it is just background noise, as many shows are (for example radio 1 in the UK) then general chit chat with light news etc is probably okay. Some DJs can put there own personality on the show, but the music can be simple pop.

I think this changes when you get to more serious music shows such as that given by the late John Peel en.wikipedia.org. His show was about introducing new and underground music. Then the music is critical, combined with the expertise and credibility of the host.

*their own personality

People always hold up John Peel as the ideal, but who's the modern-day, or closest to being the modern-day Peel? In the past I've heard Bachmann on Vinyl Tap, which I like, but he's exploring a whole different thing (music history, theme shows) than Peel was.