Bought ship does not appear when mil. prod. at 0%

That has always been that way.

I think you could argue that even if the ship is bought, you have to expend some production in the form of logistics to actually crew the ship and get it into orbit.

It has to do with game mechanics. Regardless of the cost of a ship, the game always has to devote at least some military production to building it, even if it's just one little shield, and even if it takes just one turn. Without it, it can't be built no matter what you do. All buying a ship does is reduce the cost of the ship to 1 BC anyway.

This is also incoherent with buying buildings, which get finished even if the social production is 0%. You even get all of the benefits of the building immediately. For social production: Why doesn't the game, here too, just reduce the price to 1 BC and the building is finished the next turn? - because it makes no sense!

I'm not suggesting to have the ships bought and ready to go on the same turn, but when the ship is bought, I expect it to be delivered in the next turn. Don't mind being billed a bit more for "logisticst an putting into orbit"

Such a (perfectly logical) correction to the present system would also avoid fumbling with the slider, just to make sure every affected planet has at least 1 BC going to military production. I think the arguments in favor of this slight change are stronger. The current system is incoherent and counter-intuitive.

If this is the case, I definitely agree. You can instant-build social things if you have no production, so why can't you at least have a ship the next turn?

It's never come up for me, since any time I'm building ships I usually am doing it at a planet that has military "shield"-priority.

It does not hurt to have military spending at 1%, just as a general rule of thumb.
Any unused military production gets shunted to social anyway.