Each new block (even if the only transaction it contains is the block reward) is another confirmation on top of all previous transactions that have already been added to blocks.
Hmm. 140 years from now when the block reward is 0 BTC, will miners still be required to add a 0 BTC block reward transaction to the blocks? Is that a requirement of the protocol?
Yes. For a block to be valid there must be exactly one coinbase tx per block. Not zero, and not two or more. The value of the coinbase must be equal to the block subsidy plus the sum of the tx fees (technically the sum of the outputs of all tx in the blocks minus the sum of the inputs of all tx in the block). So for a future 0 BTC subsidy block containing zero transactions the coinbase would need to be zero. Of course there is no economic value in hashing to find a zero BTC coinbase block so it would make sense for a miner to simply go idle until one (or more) unconfirmed transaction appear on the network. Still I doubt that will ever happen. If Bitcoin is still around 140 years from now it is highly probably the memory pool will never be empty.