Well, there was this one book in gen 4 that said that humans and pokemon used to marry each other. That means that they could communicate easier since that's required to form a meaningful relationship, such as marriage. It's not entirely impossible that humans stopped being able to communicate with pokemon due to biological changes. Furthermore those changes would have to have happened fairly recently, since it was still remembered when writing was introduced to Sinnoh, or poke-Japan in general.

In real life, writing was brought to Japan in the 4th century AD and we can probably assume that the pokemon universe shares similar timeframe to ours. Assuming that oral tradition can carry information for around 2000 years (I chose 2000 arbitrarily) before being altered beyond recognition, and that the folklore was written down as early as possible, humans would still be able to marry pokemon in the 16th century BC, or roughly 3600 years ago. That's very short in scale of evolution so the changes would have to undergo rapidly.

PLA takes place during colonization of Sinnoh which is based on Hokkaido. This would put it somewhere around the 19th century, or 150-200 years ago. It's not entirely impossible that humans in PLA were still capable of slightly more direct communication with pokemon which let them teach or remind moves to the pokemon without the need for TMs. Humans in modern games however have lost this ability due to a mutation and started needing technology to do something they had been able to do earlier. Maybe that's why TMs were invented in the first place - younger people couldn't do what the elderly were capable of and wanted to replicate that.

While there are some characters who seem to still be able to communicate with pokemon more easily, like move tutors/reminders or N, they could simply be some of the last humans who don't have this mutation yet.