I would say I totally agree, not because I've experienced it, but because I have read enough forums and seen enough BRS videos lol. I just see a lot of people with perfectly good tanks, but they are chasing a number or going over to fight a smaller problem, then they end up with a huge crash. I think one video in BRS explained it really well as a microscopic warzone that goes on in your tank, that you can't 100% control, but you do influence.
Anyways, keep in mind that when you are testing for phosphates or nitrates, this number is what ends up coming out AFTER the nutrients are used. So you likely do have a time when your phosphates and nitrates were spiking up but were being used by the algae as a food source, then sometime after this you test and it reads as zero. But without a food source, they wouldn't be able to take hold, so we can visually know that they get above 0. Now the issue with just removing all phosphates and nitrates from the system is that cyanobacteria then can take hold because it thrives in very low nutrient environments since the other algae then aren't around to out-compete it for space and those nutrients. This is why they tell you to at least keep your numbers above 0 slightly.
I think the biggest issue here, is that like you said, you were trying to chase that greater than 0 number, but your algae was able to consume it too fast for it to actually increase anything on your reader. Basically just fertilizing your algae more and more until you finally got above what they could consume in a day. These types of methods probably get different results in more established tanks, but that is because they have more predators/competition than you have currently.
What I would recommend, is adding something to compete with it that is hardy, and add something that will be a predator for it. I wouldn't say this because of any personal experience, but because that is what the advice that BRS typically gives to these things. You could do this in various ways, adding some refugium algae to the tank that is more appealing than what you were dealing with currently, I have seen work on other tanks (like pompom or sea lettuce is something I've been very interested in). You could add some copepods/phytoplankton. The copepods/phytoplankton BRS has a really good investigation of new tank syndrome with them specifically. The copepods will eat the algae, and the phytoplankton will compete with the algae for food. You could also add a tang if your tank is big enough, or maybe you could find an LFS that will let you take a little one and trade it in when it's bigger. There are other algae-eating fish though, but they seem to be the best. These will just consume it all day, keeping it at small enough numbers, allowing other things to finally get into high enough numbers to out-compete the algae.
Though if you go with the above method, especially if you do more than one or go aggressively with any of them, you may need to continue to dose phosphates and nitrates. I'm not really sure TBH, it will depend on your setup, how much of what you add, how much phosphates and nitrates you will consume, and how much your tank is producing. This is why I believe BRS suggests getting monitoring devices. You can see the ammonia go up, then the nitrite, then the nitrates/phosphates, and then go back down as they are used up, like in real-time. It gives you a better idea of when and how your system is doing the end of the cycle.
