Currently, NASA is investigating the use of hydroponics, aeroponics, and other low soil techniques to grow regular plants for consumption and oxygen generation/CO2 removal on long voyages in space. Why is this? Aren't algae more efficient than land plants? According to Wikipedia, typical crops have a photosynthetic efficiency of 1–2%, while algae have an efficiency of 20-30%, which is much better. Algae is also a decent source of protein, carbohydrates, and fat, and if it lacks certain micronutrients, the astronauts could be given supplement pills to make up for that. On earth, plants may be more efficient, as you do not need that much specialized equipment to grow corn or potatoes, while much expensive gear is needed to grow algae, but in space, the land plants would also need expensive gear to grow. Wouldn't it be most effective to feed the astronauts a steady diet of algae paste?
If it was purely a matter of statistics, you'd be right. There are proteins, carbohydrates and a much more efficient photosynthesis ratio to consider here, but as always the devil is in the details.
In 2013 there was a German study into algae derived supplements and it was found that some of them were actually toxic. There is a toxin called Microcystin that is created by blue-green algae for example that can do lasting damage to the human body. It should also be noted that not everything that is called a protein or a carbohydrate is necessarily healthy for you.
Take for instance Alcohol. Technically speaking, it's a complex form of carbohydrate - C2H5OH and as such should be good for you, right? We can certainly metabolise it, but there are many organic molecules (CHNO compounds) that are bad for us and even toxic to us by virtue of the fact that they interact with our bodies in ways that either inhibit good functions or promote poor ones.
Add to that, Algae is essentially water borne, meaning that you need water as a medium in which to grow it. Water is heavy, and as such not suited as a medium for food. Hydroponics, if designed properly, only need to be supplied with enough water for the plant to absorb for its health and growth, whereas algae needs more water than that in which to actually live. That means that while it may have advantages in photosynthesis, it's possible that the water requirements make it too heavy for the efficiency gain when being launched into space.
Finally, have you ever eaten algae? Ever tried the spirulina supplements out of a health shop. They taste terrible. You really can't make people eat that long term if they are to keep their morale up.
More conventional hydroponic crops provide a variety of nutritious plants to eat, provide astronauts with a more 'natural' food experience (especially important on a long term mission where they already feel disconnected from earth), are likely to use less water in the long term, and perhaps most importantly have already been through decades of research to ensure that they are safe as a food source if grown hydroponically.
It is entirely possible that algae may one day be used in the manner you describe for a space mission, but to date there has been only a small body of research conducted into algae as a food source and much more research needs to be done before it is adopted into space programs where the risk of failure is already high and food needs to be removed from the risk list, not added to it.
Taste, texture and variety override pretty much anything else. Eating is one of the great pleasures in life. For long voyages with non professional astronauts this would be a huge factor.
Also the more different foods you have the less dependent you are on particular ones. Quite apart from the scientific knowledge gained from the attempts. At the end of the day a single point of failure should never be countenanced if it's avoidable. Especially in Space, you cannot just replenish even basic supplies.
Tim B II excellent answer covers many good points, I'd like to add a couple more that I think are key.
Growth Have you ever actually tried growing algae? It's not easy trust me, they grow in liquid medium and each species has specific requirements; now, you might say, well this is true for plants as well, and you'd be rigth, sort of. Requirements fro growing algae are actually way narrower. Many of them need PH and temperature range that aren't allowed to fluctuate much, else you can quickly lose your entire harvest and end up with a stinky liquid full of dead stuffs and toxins that you need to dispose of. Screwing up plants is not even remotely as easy.
Medium Algae, as mentioned need a dedicated growth medium which qualities need to be finely tuned; to adjust stuffs like PH and Micronutrients you need strong acids and bases along with high purity elements and compound that need to be imported or chemically sinthetized in loco. Plants on the other hand grow on dirt and, perhaps surprisingly, most regolite on nearby planets/moons is actually good enough for it(you just need to add water)
Contamination Algea growth medium can easily be contaminated with toxic microbes that compete with the algae for resources. Sterility requirements are way more stringent for algae growth