Since you're speaking to a distribution scenario where nothing ever gets opened and everything is sealed, I agree the risk is low: for cross contamination to occur, only actual risk of cross contamination is if a forklift were to punch the cheese pallets open and then immediately punch into the meat and then send it to a customer. Even if that were to happen, simple checks for package integrity prior to shipment can address the issue.
That said, GFSI codes are written to cover so many facilities that they have to call for zero chance of violating a principal. Segregation of allergens is hard written into many schemes as an intended fool proof method to avoid allergen cross-contamination. But if you're strictly a distribution facility, you can write your program to address the potential hazards, and so long as there's evidence of you following your program, it should be fine.
Take SQF for example: in their code for Allergen Management for Distribution sites, they call out 2.8.1.1. It does not specifically state segregation as a requirement, only stating "[t]he allergen management controls shall be based on a risk assessment and include the identification, labeling, and handling of allergen-containing product, including product recoup, to prevent inadvertent cross contact." For that example, you need a risk assessment identifying how cross-contamination would occur, and how you prevent it. Part of that can include your hold program, placing packages on hold if they're damaged or seals are broken, and investigations to show no other products were contaminated by the unsealed.
Segregation is easier, but if you go through the steps to prove you've eliminated the chance of cross contamination, then proudly display your program to auditors and defend it when questioned.