The most common use [of affusion], however, was for ill or dying people who could not rise from their beds. It was consequently known as "baptism of the sick". Receiving this baptism was regarded as a bar to Holy Orders, but this sprang from the person's having put off baptism until the last moment—a practice that in the fourth century became common, with people enrolling as catechumens but not being baptized for years or decades. While the practice was decried at the time, the intent of the criticism was not to encourage baptism by immersion, but to refrain from delaying baptism.
In the fourth century, a widespread practice arose of enrolling as a catechumen and deferring baptism for years, often until shortly before death, and when so ill that the normal practice of immersion was impossible, so that aspersion or affusion—the baptism of the sick—was necessary.
I find myself at a loss to come up with a motivation or explanation for this alleged behaviour. From a post here by James T I understand early Christian communities may have imposed fairly lengthy periods of instruction for catechumens—even a period of three years would be "nothing particularly special", according to James. The intent, on the part of the receiving church members, was to ensure the converts' beliefs were both sincere and orthodox. However, this doesn't explain why the converts themselves would want to defer their baptism for so long after the mandatory period of instruction. Even presuming that someone sought a Christian affiliation only to improve their social status, as Augustine of Hippo condemned, what advantage was there for them in remaining unbaptised? And if such a person was insincere in their beliefs, why bother with a deathbed baptism at all?
So in summary, my questions are as follows:
Is it true, as the articles above state, that it was common in the distant past for converts themselves (i.e., not the church) to delay baptism for decades, or even until shortly before death?
If so, what were their reasons for doing so?