Does a low profit margin on mining reduce the integrity of the blocks stored in the transaction history?

As the mining Bitcoin payout decreases from 50 to zero, what incentive is there for miners to continue operating?

Is there a need for miners to continue to operate when the payout decreases to zero?

I thought part of the purpose of mining is to validate the Public key with the General Ledger that is replicated in P2P fashion between nodes. If the miners go away, will GL validation stop?