You are confusing MTBF and lifetime expectancy.
The former is about random failures of a device while the latter is about how long a device is expected to last. Those two can be very different.
For example given the 2003 "life table" for the US - a 30-year old has a ~0.1% chance to die in that year - this translates to a MTBF of roughly 1000 years, however even the best wear out long before that - their lifetime expectancy is a mere 49 years.
So MTBF expresses really just a random chance to fail and thus does not require any life time tracking.
If you were to implement some form of that (e.g tires lasting only X landings), then you'd need indeed some form of air frame state save.
In reality, you'd also hope that maintenance is aware of the lifetime expectancy of the various devices and replaces them before that.
So I don't think you would gain much by tracking stuff across flights, unless you want to implement some sort of maintenance simulation, i.e. replace engines after X hours (depending on usage), etc. along with the financial impact to enable some kind of "running an airline" experience.
In this simulation MTBF is really just there to give you a better idea of what to expect, i.e. a MTBF of 20h would mean you should expect one failure in 20h of flight (or 5% per hour, or adhering to how it's programmed: 0.0139% per 10s ) regardless of how those 20h are composed. Since it IS random however, you might experience 20 faults in 10 hours or none in 100h.
In reality the MTBFs are much higher of course and vary from system to system as well, while here it's all combined into one.