transaction costs will be the only source of income for miners. to keep the miners alive throughout the world should use digital currencies as the main medium of exchange, so it is likely that transaction costs will rise due to increased demand for the transaction.
The problems is the block size is quite full at the moment. It cannot support more transactions, so people will not use bitcoin.
It's not quite that full yet; a normal transaction will usually be processed within one or two blocks, and backups in transactions usually only happen after a hashrate drop or a big gap in blocktime, and those are usually fixed very quickly; it won't drive people away, but transactions are arguably more secure in Bitcoin than most other payment systems.
Of course, there will always be more BIPs that can increase block size or whatever we'll need in the future; either way, what needs fixing will eventually be fixed.
Sometimes if there is a big gap in the block time, there will be a big hold up in the mempool. If the block size is 2MB, the problem will be less severe.