There are two basic schools of thought. Then old school is to run a chain and sprockets until you can't. The prevalent approach these days is "preventive" replacement of chains before the sprocket is too far gone. You may believe that then wear pattern is such that a new chain will work even after the prior chain is "stretched" 1% (1/8"over 12"), but the cumulative experience of thousands upon thousands of riders indicates otherwise.

BTW- your theory that the stretched chain rides out toward the tips of the teeth is flawed. This applies to chains running at high speed and low torque, A bike chain is opposite, running at low speed with high load. The engaged rollers reach maximum load at about 11:00 as they're rising toward the top. At the moment the chain isn't pulling at a tangent, but on a secant, pulling the roller in and down to the root of the tooth. It then does roll up nearer to 12:00 as it approaches disengagement, but it's the root wear, not the tip wear that causes skipping.