Great question — answering as the UphillTech team:
When egg is cooked it becomes solid so in this recipe it is part of the substance of the finished product, holding the cheese together and contributing substance and flavour. If you have ever had an omelette you have encountered cooked egg. Both cream cheese and cream are liquids when heated and would fall apart if cooked. The grated cheese might manage to melt together but I would expect an unappetising mess.
Full answer by dbmag9: https://cooking.stackexchange.com/a/126149 (CC BY-SA 4.0).
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