controlling silicate is a good idea. but eliminating it to eliminate algae may not have the desired effect. i bet corals need some silicate for normal growth and skeleton production. you take out too much silicate you harm the corals.
the tough thing to understand i guess is that there are levels of chemicals in your tank that you will not be able to see. but the organisms in your tank can still use those chemicals - it doesn't mean the chemical or molecule is no longer in your tank.
overall, controlling any chemical will take extra money. for some people this is not an issue, but why waste all that money trying to get lab-grade reef water when you can save it for great livestock down the road.
you want to know why algae grows? ID the algae, bacteria, or protist and see what online sources say. they will usually say specifically that phosphates, or nitrates, or silicates or something else is being used. in reality everything is being used because these are living cells. but what differentiates them in your contexts is what they mostly like to use. like your diatoms - they like silicate apparently.
controlling ich and controlling some nasty algae are a whole different ball game. diatoms are nothing compared to bryopsis. i've had both. don't forget about the lovely cyano. i had that too. Everything can be treated and waited out. ich is easily preventable by quarantine. algae is not. you will get algae no matter how much you pick at your frags. it will regrow. and then you'll have an epic battle on your hands like i did with bryopsis many years ago
your diatoms are very nice food for most CUC animals. if you got snails and hermits in there they should be helping. emerald crabs can be useful in eating bubble algae and hair algaes (when hair algae is killed by peroxide). so having a good CUC is very important for a reef tank.