Pillagers cannot use bows, and both all types of skeletons and Illusioners cannot use crossbows, even though both are weapons that fire arrows. In the case of Pillagers and Illusioners, it has already been reported (MC-139433), but for skeletons, it was discovered by Minecraft YouTuber Phoenix SC (www.youtube.com/watch?v=McU0QILC4_o), and I discovered it works with ALL skeleton variants (screenshot below). In the below screenshot, all skeletons are using their melee attack (they normally don't get this close to mobs they are hostile to (barring the wither skeleton, who normally attacks with a stone sword)).

The steps to reproduce are exactly the same as in MC-139433, except that you can use "skeleton", "wither_skeleton", or "stray" instead of [illager], and that this NBT data is instead:

{HandItems:[{id:crossbow,Count:1b},{}]} or {HandItems:[{id:bow,Count:1b},{}]}