There are a plethora of synonyms for the phrase "foolish quest" that one can use to convey similar meaning in writing or conversations. Some of the commonly used alternatives include "wild goose chase," "fruitless pursuit," "foolhardy mission," "senseless journey," "unwise adventure," "frivolous crusade," and "futile expedition." All these synonyms embody the idea of pursuing something that either has no potential for success or is not worth the effort. Such pursuits are generally considered wasteful and often involve taking unnecessary risks without any apparent reward. Using these synonyms adds depth to communication and can help reinforce the message you're trying to convey.