My Knowledge of CS:
If you leave a call spread expire, the shares should be assigned on Saturday following Friday expiry. The short shares will always be assigned. There is a remote chance the long shares will not be assigned. You would not know this until Monday morning. If this happens then you are at risk of the share price changing before you sell the shares. My broker does state, in writing, that a call spread can be left to expire. The customer does not have to initiate settlement.
I bought one call spread in November. It was Amazon, 370/375 spread. 1 block. Expiration DecWk4, about 1 month out. Bought when pps was about $372. When the stock reached $376 (after about 3 days), bought to close the short shares. Held the long shares until the stock reached about $394 and sold for a nice gain. I could have held all shares until expiration and made about one-third the profit.
I am a peep so take my thoughts with a grain of salt.