When I transited BOM (onto an AI domestic flight) I needed to retrieve bags in BOM and recheck them (fast process). Similar as when entering US.

You can get the bags checked to HSR. That isn’t the risk. The risk is the BOM flight is delayed and you miss the AI flight. If it is a single ticket they will protect you on the next available flight. If it is a separate ticket you are out of luck.

Having said that, in many cases two tickets is way cheaper so doing a risk assessment is normal.