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1. The suzerain’s army has no food and grass in the vassal territory.
2. Cannot forge the CB that vassalizes neighboring countries.

1. Yes unfortunately that is an issue with all allied, vassal, suzerains territories. You will have an easier time "finding supplies" on enemy land. So yeah even if allied and keeping their lands safe you won't be given anything and attrition is going to be a problem.
2 You can always fabricate claims and vassalize through the piece deal, instead of annexing. If the enemy is small enough, below 100% warscore.