The airlines scheduling software does track this, but it has two serious limitations...
1) GIGO: Garbage-In, Garbage Out. If the times are entered erroneously, it won't keep you legal (the pilot is ultimately still responsible for this). There is always the possibility of mistakes, and if for some reason the actual flight times don't make it into the computer, the schedulers may just enter the scheduled times (they are not going to lift a finger to attempt to find the right answer).
2) Time-late: The software may not flag a violation until after the times are entered...at which point it's too late! In the 121 world, if the computer flags it, you WILL be violated...the company will immediately report you to the FAA to ensure the blame gets placed squarely on you, and not them.
Also there are certain morally bankrupt companies which falsify the computer records on an occasional or wholesale basis. There are several incentives for this...
1) Control on-time performance.
2) Avoid delays or CANX due to timed-out crews.
3) Long-term you can get more productivity out of your pilot group if you fudge all the numbers a little...fewer monthly/annual timeouts.
For this reason I learned to keep my own logbook. The company ALWAYS backs down when confronted with this...if they force the issue and an investigation ensues, airplane trip cans and other crewmember's logbooks may get scrutinized and compared to the company computer
