You are correct. Your method of keeping the starter will over time select the culture that is best suited for your method of keeping, from available gene pool.
Reminds me of a story I heard of a beer brand (forgot which one) that opened a new factory which was heavily modernised, but decided to take the wooden roof from the old one and install it above the copper kettles in the new location to make sure the environmental bacterial cultures would remain the same to keep their "flavour identity"
Anecdotally, my experience has been that while yeast cultures are durable, you can also get some maladaptive selection going from time to time; eg, if you are too irregular in feeding your starter, you might end up with a slow-growing culture rather than the fast-growing culture you get from feeding your starter twice a day and want for a good rise. Your starter will still be alive, but not as useful until you start feeding it constantly again and get that fast-growing culture established again.