What is the fastest way to transport large amounts of block a large distance without hoppers?

Don't count on fully automatic system - there's a pretty unlikely scenario where it would be semi-practical: if your farm is very close to an end portal and the destination is very close to world spawn, a player afking in the end could keep a pipeline from the obsidian platform to the return portal loaded. But that requires a special foresight when choosing the locations. The other scenarios involve chunkloading the entire route, which involves building a chunkloader line along it whole. It is practical for distance of ~5 chunks, a pretty bad chore for ~10 chunks, and with 60-ish chunks distance through the Nether, a completely impractical gigagrind.

More practical options are based on player-loading the transport.

• Ender pearl stasis chambers, and transporting the items by filling inventory and enderchest with full shulkerboxes.
  Permaloaders keeping the stasis chambers on both ends loaded, and triggering the return in one of the following ways:

  • Wireless redstone tricks, like a sitting tamed wolf anywhere in the world standing up when a player goes into the Nether
  • Redstone timers, for example, ones that trigger return after a minute which you spend filling your inventory with shulkerboxes, and setting up the stasis chamber in the opposite direction
  • A friend to trigger the return in multiplayer

• Player-loaded railway line through the Nether. Send multiple full chest minecarts into the Nether, and stash them in a PEZ dispenser right after the portal they arrive through (at most 1 chunk away from the portal).

  Example minecart PEZ dispenser:

  

  Note the carts will only stack like this if they land on a regular block, not on a rail. The slab attached to the sticky piston will eject the carts in sequence, pushing them onto the rail one after another, when the clock behind the piston is active.

  Add a regular minecart to the top of the stack. Activate the clock, and board the last minecart. Have another portal and another PEZ dispenser in the overworld at the other end, so your carts will form a neat queue instead of a typical mess if you let them run into each other on a rail.

• A caravan of llamas. Or several caravans of llamas.
  Good llamas with 9 or 12 slots are hard to come by, but if you breed enough, you can - at rather leisurely pace, say, riding on horseback - pull the "leader" llamas of several caravans of llamas on leashes, and transport enormous amount of materials in one move.

• If you're very technically inclined (building an update suppressor is something you're proficient at), you can utilize the recently discovered item shadowing to transfer specific types of items an arbitrary distance. It's a complex technique in which the player suppresses update of a floating comparator popping off as contents of the chest it reads change (player inserts a stack of items into the chest), creating a "shadow copy" of this stack of item in player's inventory while placing the original in the chest. Adding or removing items to/from one of the pair of stacks is immediately, identically reflected on the other regardless of distance, so one can add items to one instance of the stack at the farm, and drain them at the remote storage from the second instance transporting them an arbitrary distance instantly.

A flying machine with stacked minecart chests can transport large amount of items fairly quickly.

This video is a good example of how to build such a machine.

If you don't mind travelling with it to make sure it doesn't stop anywhere because of unloaded chunks, minecarts with chests should work just fine, but there's not really a good way besides hoppers to get them from point A to point B without a despawn risk, ofc shulker boxes with ender chests are discluded.