If you read through the boeing procedures, if an engine fails just after take off you delay cutting throttle or hitting the cutoff until you have positive climb and pass a certain altitude. Specifically because a mistake here would be so incredibly catastrophic. The following number of steps and verbal cross checks for then shutting down the engine are quite daunting. Not something applicable here, but still interesting to learn about

Would it matter in this case since you would crash either ways. I’m talking about protection in a very specific situation where you make it harder to shut off both engines when you’re very close to the ground.