Anyone know why my crossbowman gets insta-killed here?

Civ abstracts a lot of things to make it work on such a grand scale. Till walls get obsolete you can say that they are higher than the environs so they shoot from above - either with bastiae, longbows, crossbows, cannons, depending on the era.

The city attack/health bar was first added in Civ 5 as an idea. Its main purpose was to mostly help the AI - it tends to throw away its units too fast, so having such a static garrison helps slow down the player and give the AI some time to find/buy/bring over new units to the fore. It is not perfect but it does help the AI. :)

It helps the human player way more, chiefly because the AI is so terrible.

I have two Legions (one stacked with a siege tower), two archers, and a warrior adjacent to your walled city.

Who does it shoot at?

The warrior

I now bring a Sacrificial Warrior to all sieges
 
@aieeegrunt
I wish I had your luck - the AI in my games always goes for the artillery and tends to have also a ranged unit within the city. In your example you actually did not have any artillery so the AI went for the weakest unit. At what difficulty setting do you play usually ?
 
It helps the human player way more, chiefly because the AI is so terrible.

I have two Legions (one stacked with a siege tower), two archers, and a warrior adjacent to your walled city.

Who does it shoot at?

The warrior

I now bring a Sacrificial Warrior to all sieges

Interesting - my anecdotal experience is it would tend to shoot at the archers first (which is why I rarely use archers against walls at all).
 
@aieeegrunt
I wish I had your luck - the AI in my games always goes for the artillery and tends to have also a ranged unit within the city. In your example you actually did not have any artillery so the AI went for the weakest unit. At what difficulty setting do you play usually ?

Either Emperor or the one above it. The one where the AI already had three cities before I could found my second lol.
 
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