Then again do we have to dose extra P for healthy growth and to keep algae in bay.
That is a question we cannot answer for you. Is it possible you have enough P from fish food (and thus fish waste) alone? Yes. There are low tech purists out there that add nothing but light and fish food. If done carefully, this can be all you ever need.
Is it possible you need more than your fish food can provide alone? Yes. Given the number of people adding PO4 fertilizers (KH2PO4 or otherwise) to their tanks, this seems to be common, particularly in the high-tech end where nutrient use is quite high. (edit: yes, I know you specified high-light, I wanted to illustrate the range of possibilities, low-tech to high-tech.)
Getting a solid answer depends on a number of hard-to-measure things. You'll have to experiment with your tank, as the answer is going to be different from tank to tank. The same holds true for nearly every nutrient in the planted tank. There's rules of thumb out there, but if you want exact need levels, that takes personal experimentation with your specific tank conditions.
Fish food adds PO4. But even the simple question of how much total PO4 you are are adding depends on how much fish food you add, and what kind of food (different kinds have different concentrations of PO4). This is relatively easy to measure, but takes some calculating.
How much of that PO4 makes it to the plants is harder to quantify.
The tank inhabitants will eat some or all of the food. Of whatever the inhabitants consume, they'll use some of the phosphorus, and excrete as waste the rest. How much they use vs pass depends on things like breed, health, is it growing, and even how much it is being fed. Assuming you remove the inhabitants when they die, the PO4 they use is never released to the water column.
Any overfeed not eaten by the inhabitants is comparatively easy to account for, as it will eventually rot and make it straight to the water column. However, that involves knowing how much isn't being eaten, which might vary from day to day.
Of course, adding vacuuming, water changes, etc, removes some of this PO4, just to add a few more variables.