Upvote:1
Only if they do not want to pay import duty (and tax) on them when they re-enter the country with them.
The key words are 'may elect'.
When you re-enter a country you can be asked for proof that you had your valuable items before you left that country for travel. Registering is a way to do so. Often proof of sale will also work.
As far as I understand the system you only need to do it once for each item, as you do it to proof you owned it in your home country, it does not matter how often you take it abroad.
Most people will not do it for items which are obviously used for a while as customs officers will not try to charge them for 'importing new items' as they are clearly not new items. But to the letter of the rules, you may be charged import duties even on older items. So if your possessions are valuable, you should get the paperwork sorted.
The text you quote gives two ways to get proof of ownership in South Africa, and the strong advice to do so for items over the value of R50 000 by using the form available from banks.
As I read it, it is not required to get the form, only that for items over that level the bank form is the usual way to handle it.
And registering is not unique to South Africa, it is the same for most or even all countries. The option to register at a bank is not that common, which is likely why in many countries proof of sale to you is accepted.