Stated purpose of SGB when it was launched by Govt was to wean away people from investing in physical gold for couple of reasons:
- Reduce gold import. Gold import forms substantial dollar outflow. If this is reduced, current account deficit can reduce or be more manageable
- Investment in physical gold is non-productive. SGB provides people to get gold exposure and govt can use that money for productive uses (assuming what govt does is productive
)
Why not gold ETF or other means
- As rightly pointed out above, ETF still results in import of physical gold. SGB are backed by sovereign guarantee only
Seems like you haven’t read any offer document where explicit mentions are made 
Having said that, by issuing SGB, RBI is taking gold price movement risk on its book. But RBI already has tonnes of gold reserve (which is necessary) so risk is kind of hedged.
For user it has govt of India guarantee. If that doesn’t fill safe then using Indian currency note should feel risky too
- Per govt, Average user buying gold may not be sophisticated. So simple product was invented (which can be bought even without dmat) with sovereign guarantee and extra 2.5% interest to make it more lucrative.
All in all, it is risky product for govt. (actual payout for initial SGB is much more than govt borrowing rate). But idea is if it can reduce gold import in long run and make money more productive, overall benefit to economy would be higher.
Hope this helps