Reason 1 — terminal value is known. It’s more than deterministic. It’s exactly $100 at maturity. Brownian Motion doesn’t match that.
Reason 2 — drift estimate is too hard too sensitive. A BM process has a drift value. U can be very careful very thorough to estimate it, but any minor change in the drift estimate would result in very large differences in the price evolution, if the bond’s lifespan is longer than 10Y.