Cost effective drivetrain maintanance With my previous bike I followed the general recommandation for maintainance of drivetrain.

This usually goes like the following: replace chain every 3K Kms, replace rear cassette every 6K Kms and after 22K Kms I replaced the chainring as it started to show shark fin teeth.

I am asking what is the most effective method to maintain the drivetrain, does the above procedure which involes quite a bit of money and labor ( not to mention that I have to get my hands dirty with grease in the process ) or simply use the drivetrain until starts malfunction at which point simply replace all the parts: chain, cassette and chainrings?

Supposing that first sign of malfunction would appear after 11K kms ( half of what I got with previous method ), I could replace the wholedrive train and get another 11Kms at lower cost, not to mention that I don't have to get my hands dirty and I do the procedure only once compared to seven times.

Would the approach work? If so, why do get other recommandations in media, books, etc?

Edit

I feel that one can answer the question if we could somehow look at a chart that plots the performance of the drivetrain compared to the distance used. As some suggested performance would include power transfer efficiency, probability of hazards, noise, shifting, etc.

As I see it chain skipping has a high probability of hazards as it could fall of and cause the rider to crash, so that would score something like 9 out of 10 for probability of hazards while a new chain would still score something like 1 out of 10 ( there are chains that brake brand new ).
Make the small investment in a chain checker ( I like park tools CC-3.2). I would generally recommend one of them that measures the chain based on length rather than lateral deflection. Each manufacturer will probably have it's own recommendation, but a safe bet is to always replace your chain before '.75' (75% wear). This will maximize the life of your cassette and chainrings as they will not be ridden on a stretched chain. It also eliminates individual variation, as some people will stretch a chain more or less over a given distance ridden ( some people like to mash and others like to spin).

It is also a good idea to keep your chain clean, as a dirty chain acts like sandpaper as it is cranked over the teeth of the chainring and cassette.

By simply replacing the chain at the proper intervals I have made cassettes and chainrings last years of frequent use. I don't know exact numbers but they would be pretty meaningless as they vary with rider and conditions. Certainly more than 2 chains per cassette.