Relays are actually quite cheap now! They used to be a bit more expensive when they archived all the traffic, but in sync 1.1 that was dropped and they can be run on $20/mo VMs pretty trivially now
If I read a post from a month ago, how will my client know how many likes it has or what the replies were? Without reverse links, someone has to look up in a database of all AT actions for likes/replies pointing to that post.
Contrast with the inbox/outbox forward/reverse linking model of activity pub.