A true fixed bankroll means that you will never, ever, ever, be able to replenish it. If you lose it, you're at, best, out of the game forever, and and worst, you're living on the streets, because your bankroll is what you used for food and rent.
If you start with a full Kelly fraction (for optimal bankroll growth), but never resize bets, you have a 13.5% risk of ruin. Most people are more careful than this if the bankrolls are sizeable.