Pillagers with Multishot or Piercing crossbows don't have the enchanted effects

If you use a command to summon a Pillager holding an enchanted crossbow, you'd expect that the crossbow would have its enchanted effects in a similar way that skeletons with say Punch II on their bows give increased knockback.

The following command summons a Pillager with a Quick Charge III crossbow. If you switch to survival mode or summon a villager or iron golem for it to attack, you will find it does indeed shoot much faster.

/summon minecraft:pillager ~ ~1 ~ {HandItems:[{id:"minecraft:crossbow",Count:1,tag:{Enchantments:[{id:"minecraft:quick_charge",lvl:3}]}}]}

However, the Multishot and Piercing enchantments do not seem to cause its enchanted effects to carry over to the Pillager - Multishot will not cause it to shoot multiple arrows, and Piercing will not allow the arrows it shoots to pierce you and hit other mobs or players behind you.

/summon minecraft:pillager ~ ~1 ~ {HandItems:[{id:"minecraft:crossbow",Count:1,tag:{Enchantments:[{id:"minecraft:multishot",lvl:1}]}}]}
/summon minecraft:pillager ~ ~1 ~ {HandItems:[{id:"minecraft:crossbow",Count:1,tag:{Enchantments:[{id:"minecraft:piercing",lvl:4}]}}]}