On one hand, a biological resource system should be avoided because they are large and energy intensive. On the other hand, it is likely necessary due to the complex biochemical requirements of humans.
Recycling O2 and H2O are technically easy. But we do not live on O2 and H2O alone. There are many essential micro- and macro- nutrients which must be provided. But “essential” is species-specific and there is no assurance we know them all. There may be, for instance, a coenzyme we have yet to identify. Sending humans on a prolonged space voyage with a synthetic diet would be a perfect way to discover “space scurvy”.
Algae is a promising “Space Food” since it can be grown from inputs of inorganic salts, CO2 and light. Since algae are metabolically vastly more sophisticated than humans, there is a reasonable chance they manufacture the mystery micronutrients we have yet to discover.
Besides palatability problems, there are significant resource problems growing algae in space.
They are energy inefficient. Only about 12% of incident light is captured. They require a “Goldilocks” range of light intensity. Too much is toxic. Too little and they don’t photosynthesize. Solar radiation is very difficult to utilize for a light source, so the bioreactor becomes a significant drain on spacecraft electrical supply.
Due to self-shading, algae require a narrow range of suspended concentration in the growth media. This means a significant mass of media is required.
I worked on a project to build an Earth-based algae system to generate medical oxygen for isolated clinics in developing countries. The system required a cubic meter (one metric ton) of media to provide O2 for a single person. This is similar growth media requirements as the algae demonstration in the ISS. https://www.nasa.gov/mission_pages/station/research/news/photobioreactor-better-life-support
Another problem is growing algae in zero-g. On earth, bubbles are a convenient way to segregate gasses from growth media and agitate the media. Bubbles don’t serve the same uses in space.