>what is stopping us from using the same algorithm we use for training, when using the network?

Our inability to produce 1.56 trillion tokens. A human can produce ~200 tokens per minute and works for ~50 years, 8 hours per day and 5 days per week. That's 200 × 60 × 8 × 5 × 52 × 50 = 1.25 billion tokens, so three orders of magnitude too few.