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?

What is going to happen when it is totally infeasible to download the entire bitcoin transaction history?

As far as I know, the bitcoin system currently relies on the principle that all transactions are made by someone with access to the entire history of previous transactions. Since bitcoin’s public debut 2.5ish years ago, these records have stayed small enough that it’s still easy for one person to download and update it.

Once it gets large enough, though, it’s going to be hard to do that. When I ask most people about this problem they just tell me that eventually we will start trusting our money to some bank-organization-type-thing (e.g. Coinbase) and we won’t have to worry about the integrity of our records.

Imagine that in the distant future, the bitcoin system becomes widespread enough that the rate at which transactions history grows exceeds the rate of change in disk space technology. (far cry, I know, but let’s just assume a worst-case scenario.) How would bitcoin account for this problem?

Is a better, more widely agreed on solution?