Back of the envelope math:

If you measure by the product of throughput and distance traveled, for an item with a stack size of 100 (e.g. metal plates), the player's inventory adds up to roughly the same capacity as 2500 yellow belts. And that's assuming 100% utilization running back and forth in both directions, with no unused inventory space and no wasted time.

A basic assembler can manufacture 2500 belts in about 21 minutes. So as a rule of thumb, if you're playing for longer than 21 minutes, belts are worth the investment (at least for bulk transport of raw materials).

(I guess maybe add an additional factor of at most √2, since the player can run diagonally and belts are orthogonal.)

Handfeeding only has higher throughput for single trips/a single item type, definitely not for an entire factory. The player inventory and movement speed can't keep hundreds of assemblers working continuously. A high throughput starter factory looks something like this:

https://youtu.be/RI4ocNajf_w?si=O1aRi22riKwiuh_p&t=7493

A T1 belt throughput is 15 items/s. Player inventory is 80 slots (2 cargo wagons, incidentally, though players load/unload instantly).

Stack size varies, but let's take 75 as an average, which means a player can carry 5600 items.

But carrying isn't throughput. If a round-trip takes 30s, player throughput will be 186 items/s. That's a measly 12 T1 belts.