tire warning light needs improvement

I have a new car, but I am wondering why the low tire pressure light does not indicate what tire is in need of looking at.

My light came on, I went to put in air.  In NY there were quite a lot of free air tanks, here in Colorado they all seem to be $1.00 for 4 minutes.  So I take off all the caps and start to put in some air in each tire.  The light goes off, but not for long.  My ride home, the light comes back on.  I search my car for my air pressure checker thing and finally found it.  I take off all the caps and check all the tires.  I can't figure out of the gauge is broken because every time I check the tire, I get a different reading.  I get the air hose, and check the pressure that way and fill up where I think it belongs.   The light goes off.

The next morning it goes on again.  I refill a few tires, not using all of the 4 minutes.  The next morning, when the snow finally is gone, I see a screw in my tire.  Ahh.  Well that explains that.

I go to Costco and tell them I need a plug.  They charged me $3.24!  For the piece and for them to do the work.  Holy cow, what a bargain!  Costco suggests I come back after 25 miles for a lug nut tightening/check, which I had done two days later for free.

But all of those trips to the air stations could have been avoided if my car told me what tire was having the issue.