Asteroid mining is much more plausible than you think:
I propose a sequence of events that minimizes the set-up cost while maximizing the returns for processing asteroids, as I will explain:

Dust from asteroids is easy to capture and process. Experiments have proven that it can be accelerated to high velocities in electric thrusters. This gives the option for ISRU-fueled solar-electric asteroid movers with practically infinite deltaV.

A lunar-assisted capture of Near Earth Asteroids can cut off 1.5km/s from the deltaV requirements. This means the asteroid mover only needs to provide the tiny amount needed to set up this capture.

Once around Earth, there's plenty of time to adjust the asteroid's orbit.

Small deltaV requirements and plenty of time for maneuvers means cheaper and smaller spacecraft can do the job.

Having the asteroid around Earth before processing means that heavy equipment won't have to go far. Telepresence robots, human repairs, replaceable equipment...

These will make asteroid mining/processing massively cheaper than having to send a lightweight, ultra-endurant and autonomous factory out to deep space.

Dropping asteroid chunks into the ocean without actually refining it also has another advantage.

Cutting up rocks is much cheaper, energetically, than melting it. The power requirements, and therefore cost, of asteroid mining equipment can be reduced further by leaving refining to be handled by the extensive infrastructure we have already on the ground.

Asteroid mining just slots in a new source of resources into our global raw materials supply chain. This should also alleviate concerns about a 'market dump' of resources in between Hohmann transfer windows.

What do think?