I never really understood why anyone wants to maintain LRU properties in caches. It doesn't make sense today and it didn't make sense decades ago, either. You do need some rational basis for eviction, but ranking your hot set on every access was always just weird. I am glad this is being fixed in the literature lately.
What would you suggest as an alternative basis for eviction?
You can evict based on recency without maintaining LRU order at all times.
There are some difference, the most notable one is that 2Q evicts all objects from the small queue (does not move to the large LRU).