I was reading some questions on this site regarding vagueness and the Sorites

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I was reading some questions on this site regarding vagueness and the Sorites conundrum and I'm not sure I understand the fascination with figuring out what does or doesn't qualify as a heap. Isn't the word heap useful precisely BECAUSE it doesn't have a strict quantitative requirement? We choose to use the word "heap" and not a different word (like grams, or tons, or twenty-seven, etc.) because it offers us flexibility. I'm not sure exactly why this "puzzle" has received so much attention. The fact that there hasn't been an accepted solution makes perfect sense to me because there is nothing to solve. It seems like trying to apply precision to a word intentionally designed to be imprecise. It seems to me that if we figure out the exact point at which something becomes a heap then we will no longer be able to use the word as freely. Am I misunderstanding the problem? Thanks in advance!