If you invent a hash function that is two times more computationally expensive, then you will simply drop the hash rate by half.
The idea is for the hash function to delay computation by keeping the processor preoccupied with low-power, time-consuming overhead, like context switching, interrupt requests, memory and file access, searching arrays etc. But the overhead must be required for valid hash outcomes, so it can't be skipped or substituted with faster operations.
The solution you are looking for is to require a pause and to have a low-cost independent method of verifying the pause. Relying on arbitrary processes to introduce delays is not viable because technology will adapt.
The reason that ASIC miners are preferred over CPU and GPU miners is that they are more energy efficient, and one of the ways they achieve better efficiency is by
eliminating those same computational delays that you propose.