There is a difference between cache size and click speed on one side and read latency with power consumption on the other. Thus, the answer to your first question: technically (possible) is possible, but it hardly makes sense, since L3 cache memory in modern processors with a size of only a few MB has a latency of reading of about dozens of cycles.
Performance depends more on the memory access pattern than on the cache size. More precisely, if the program is mostly sequential, the size of the cache does not matter much. If there is quite a bit of random access (for example, when associative containers are heavily used), the cache size really matters.
The above is true for single computing tasks. In a multiprocessor environment with several active processes, a larger cache size is always better, due to reduced competition between processes.
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