We started implementing it like this, but it doesn't work because the "amount" in each pool fluctuates based on the volume traded in each pool and the market values of the paired tokens. So there's no good way to accurately compare the "amount" across pools with different token pairs.
Splitting the rewards is a much better solution because it allows the market to decide the risk/reward ratio for each pool.
This is true... it does allow the market to decide the risk/reward ratio. Eventually there will be a sort of equilibrium... but i think the equilibrium will likely take some time and it may appear unbalanced until such time.