Because LTV is a forecast and payback is a measurement.
LTV needs an assumed lifetime, and for a young company that assumption is doing most of the work. Estimate churn slightly optimistically and the lifetime, and therefore the ratio, moves a long way. Two companies with identical performance can report very different ratios by choosing different assumptions.
Payback asks a narrower question with a checkable answer: how many months of gross profit does it take to recover what you spent acquiring the customer. Nothing about the distant future is needed.
It also maps directly onto whether you will need to raise money, which is the question being asked underneath.