Almost all intelligent, automotive/industrial high side switches that need few external parts, such as the ITS41K0S you considered, have output delay times on the order of 100 µs – at least, as of a few years ago, when I looked.
If you can find room for a few more passives, the Infineon (International Rectifier) AUIPS7221RTRL is a couple orders of magnitude faster. Mouser is the first distributor I could find that currently has them
in stock.