If everyone start storing bitcoin and there is no single transaction for days,all miners will quite mining as without transaction there would be no reward.
Will it not kill bitcoin and make it useless?
There is always a reward for mining a block, regardless of whether or not there are transactions actually inside of it. Hypothetically something like this would end up just resulting in the market value going down since there would be a lack of people moving Bitcoin on exchanges, but a lack of transactions would certainly not kill it. As long as there is money moving, people will still care.