From what I have read I gather:
1st item that cause algae grow is lack of bacteria which occurs in new tanks.--It's not a lack of bacteria--it's the presence of NH4/NH3 (ammonia/ammonium). The bacteria consume the NH4/NH3. If there are not enough bacteria--there will be an excess of NH4/NH3--that will cause some algae spores to germination.
2nd is excess of light--Light is the accelerator and the brake. Pick your light and adjust everything else to it. If your knowledge and skill are up to snuff--light is not a problem. If they are not: Use less light.
3rd is fluctuating Co2.--Fluctuating C02 causes some spores to germination (like BBA). But generally it's not a 1 day fluctuation--it's longer term (1week or more). That's why DIY C02 users often times have more algae issues.
4th is low nitrates.--Not aware of this one other then BGA which isn't an algae. However, low/no N can cause growth to slow/stop...encouraging bad conditions that favor algae.
Am I right?
Is it possible that high phosphates can cause an imbalance which will affect the level of nitrates and or Co2?--High P04 can lead to the depletion of N which can cause growth to slow/stop..encouraging conditions favorable to algae. But High P04 in and of itself can create a buffer, so it is best to keep it within the generally acceptable range. In other words: more is not necessarily better.