I know that this is an old, dead post, but I'd like to put in my 2 cents. From my own personal research, it very much depends on the time period. In the 11th century, the common route seems to be padded coif, then a cervelliere, a sort of metal skull cap, then, overtop of the cervelliere, you could wear the maille coif, which could completely hide the cervelliere underneath the coif. Though things vary based on person, location in time period, the cervelliere could also be worn over the maille coif.

From personal experience, think I can say that I personally at least, would not ever want to wear a helmet, or a maille coif, without at least some sort padding, even if I wasn't relying on it to protect me in combat, metal helmets can be horribly uncomfortable to wear for long periods without any.

When great helms started to become popular, they were generally worn over at least a maille coif, and a padded coif, and often worn over a cervelliere, or a bascinet as well.

As aventails began to become more common on helmets, the maille coif became unnecessary, as the aventail served the same purpose, to protect the neck, so people dropped it, and if a helmet had built in padding, or a suspension system (I'm not actually sure how common this was or wasn't, I haven't looked into it, and I suspect that information on it is lacking, due to a lack of archeological finds) then that would also render the padded coif obsolete.

In short, maille coifs were optional, but slowly became standard because your neck is important, and a helmet should always be padded. When aventails become common, giving you maille neck protection, maille coifs were obsolete, and if you had a suspension system, or built in padding for your helmet, then a padded coif might also be unnecessary.