I see your point. However, if you ride aggressively, like out on country roads, or doing high speed runs it may be too late to "feel" that something is not right, unless you can feel a 10% drop in pressure which I doubt. It's always better to be proactive and know ahead of time. In cases that you described it was obvious the tires were compromised. However, if you pick up a screw, it is likely to be a slow leak. I also kick the tires, but when I am out on the road I don't want to wonder, and I don't want to stop often and kick the tires. Obviously, if I feel that something is wrong, I would stop and check things out regardless of what TPMS shows. When I am out riding, I find it really convenient and confidence inspiring being able to see tire pressures and temperatures at the press of a button.
TPMS I have is very reliable and consistent - firsthand experience for many thousands of miles. With cars, it could be different. Some cars have actual sensors which do transmit to the display unit. In other cars, the computer simply calculates wheel rpm and if the wheel rotates faster than it's supposed to, it assumes that the effective diameter of the tire got smaller, presumably because of the loss of air pressure, and then alerts the driver. I also experienced false alerts in my car once or twice.