Do you really expect me to take aircraft and passengers into the air with unknown problem after hearing loud bang and become a test pilot
Yes we do. It's what what the manufacturer certified the a/c to do, and if you hold a type rating (and considering your poor attempt at playing devils advocate, highly unlikely) it's what you would have been trained and tested on then, and unless you want a TRE to hit you, what you would do every 6 months in the sim or on the A/C on LPC/OPC.
If you do become airborne and attempt to land, or reject after V1, then you really do become a test pilot. The manufacturer of the aircraft sure as hell won't have done it.
Your aircraft is certified to fly on one engine. Past V1 that is the only thing it is safely tested (by actual test pilots) to do.
Once airborne (even only 2 or 3 feet) you then have to cut the (take-off) power control the yaw, re-flare and land. How much runway does that use? The manufacturer of your perf A aircraft never tested that and if you survive, well good luck in court.