What is my incentive for sending old blocks? If I am a miner, it makes sense for me to broadcast recent blocks since I want my chain to be the longest (see What encourages Bitcoin miners to relay blocks?). 

However, what is my incentive for broadcasting old blocks? Deep blocks are very unlikely to be orphaned, so it seems that I get no gain from relaying them, despite it costing me bandwidth.
Miners have spent money on mining hardware. The value they are able to get out of that mining hardware is tied directly to the price of Bitcoins and the mining difficulty.

If the price goes up, that will incentivize some additional miners and if the price goes down, more people will mine. But this doesn't happen immediately nor does it cancel out perfectly. Miners benefit from an increase in the price of Bitcoins and are harmed by a drop in the price of Bitcoins.

Your incentive for sending old blocks is that the utility of bitcoins drops if it's more difficult for new nodes to join the network. While this effect on the price of bitcoins is slight, the amount of old blocks you need to send is also slight.