I don't know what grammar book you are using, but actually the explanation is incomplete. It's correct for the potential form of verbs, as in the examples Majestic-san gave, but there are cases where the explanation is not correct when it's "the dictionary form of verbs". See the following example.
足を怪我してから、ゆっくり歩くようになった。
The subject was not impossible to walk slowly before injuring their leg, or it's not they couldn't realize to (be able to) do that, either. They just didn't walk slowly by their will, or didn't need to do that before. The same goes with the following examples.
勤務時間帯が変わって、朝早く起きるようになった。
相手が日本語を話せるとわかったので、日本語で会話するようになった。
大地震が起きた後、小さな地震が続くようになった。
梅雨になったので、毎日傘を持っていくようになった。
The main concept of ようになる is to express a change of the state just like "to become".
No need to do that, as mdchachi-san pointed out. It's even possible that the things you think correct are actually not correct just like this thread.
You can't do that. Please ask administrators or moderators for that case. We will do that if the thread is against our ToS (in other words, the thread will not be deleted if it's not against our ToS).