But Big-O does transmit useful information that is not captured by 'constant', 'linear' and 'exponential'. Quadratic time doesn't fall into your categorization

But Big-O does transmit useful information that is not captured by 'constant', 'linear' and 'exponential'. Quadratic time doesn't fall into your categorization, nor does O(n \log n) time. Technical jargon exists for a reason, and that reason is that it is precise and specific. It conveys exactly what it means, no more and no less. Dumbing down terminology so that everyone can understand it is a poor tradeoff if said terminology becomes vague and thereby loses meaning.