Increasing cache size grows latency in two ways: every doubling of the cache size adds one mux to the select path, and every doubling increases the wire delay from the most distant element by ~sqrt(2). Both of these are additively on the critical path, and spending more time on them would require increasing the cache latency.
The size of a cache is always a tradeoff against the latency of the cache. If this was not true, there would only be a single cache level that was both large and fast. However, making something both large and fast is impossible, so instead we have stacked cache levels starting with a very fast but small cache followed by increasingly slower and larger ones.