I am speaking about both new and old ponds with only gravel and rock on the pond floor.
Gravel and rock will have organic matter accumulate in it's large crevices, but that organic matter alone does not contain any mineral composition (clay) that adsorbs heavy metals and phosphorus. Periphyton must be exposed to the water column, otherwise once it is buried by detritus accumulation, it only becomes more decaying organic matter.
When I refer to substrate, I'm including both the organic and mineral components of the sediment layer on the bottom of the pond.
If you consider the three tanks that I have running:
Test tank has significant string algae and cold water, no plant filter
320 gallon tank has no string algae and cold water, with a plant filter
600g tank has no string algae and warm water, no plant filter
All 3 tanks have identical garden soil substrate and little to no water circulation. The 2 cold water tanks receive identical feedings of identical food. 600g tank receives heavy feedings daily. No tanks have a mechanical filtration device. The plant filter on 320g tank has a substantial clay component to it's media.
Because test tank and 320g tank are the most similar and both having slow to moderate plant growth, my observation is that the presence of clay in the 320g tank is preventing phosphorus from being available for string algae.
My explanation for no string algae growth in the 600g tank is that the warmer water is allowing for more vigorous plant growth, including some plants that are blooming, therfore incorporating excess phosphorus into the plant tissues. Frequent prunings have been required, so at that point phosphorus is exported from the system.
So - warm water may allow for more vigorous plant growth, preventing the growth of nuisance algae, but when there is cold water and low plant growth, the presence of clay is an important component for keeping a pond clear of string algae.
Because clay is a composition of minerals, it does not float, so it becomes a part of the substrate.