As far as the second part of your question is concerned, there is no debate about it. When Khilafat changes, then you must renew your pledge. Because you pledge on the hands of a particular person. This is why after the death of Hazrat Muhammad Mustafa, every Muslim was expected to get initiated again at the hands of Hazrat Abu Bakr Siddiq. There was no exception made. While they were Muslims, and they had done Bai’at at a much better hand than any hand that could follow.
So despite that fact, they were obliged to repeat and renew their Bai’at. There is no doubt about that. As far as the other aspect, the first one is concerned, I know that no Ahmadi in Qadian was ever expected, formally or informally, to get his children initiated after they reached the age of majority. Never. As a rule, they were understood to be Ahmadis and they were brought up as Ahmadis. Unless somebody renunciated Ahmadiyyat, he was not expected to renew his pledge. As far as that incident is concerned, that has a different significance.
When Hazrat Khalifatul Masih I, R.A, wrote to Hazrat Shah-e-Zafrullah Khan Sahib, that was because of Hazrat Masih Maud A.S. To do Bai’at at his hand was something quite distinctive. And that was one of the greatest favours that he did to Hazrat Shah-e-Zafrullah Khan Sahib. That he reminded him that you don’t miss that opportunity. That is applicable only to that particular situation. Otherwise, as far as the Khilafat is concerned, when one Khalifa changes, there is a time when you are not under Bai’at. In between, you are no longer under Bai’at. So, unless you renew your Bai’at, keeping somebody in particular that you will obey him, how can you continue to be as mobile? It’s quite logical and simple.