According to Probability theory and the Kelly criterion (https://en.wikipedia.org/wiki/Kelly_criterion) the optimal amount to risk is a fraction of our risk capital. We do not want our risk fluctuating around based on volatility yet that’s exactly what happens when our stop-loss widens due to volatility in the market if we are using fixed lots.
The second thing to think about is curve fitting. If we have an SL based on ATR and we are using fixed lots, that means the amount of money we are risking on each trade goes up during higher volatility times and so too does the reward. So our system training method may tend to select an iteration that had a few lucky trades during high volatility times while avoiding those few unlucky trades that would’ve made some large losses.
If we have multiple accounts then we need to consider that we should be pooling all our risk capital for the risk calculation which can get tricky as the account sizes fluctuate.