As a kid I adored Lego. I think fondly of all the time I spent playing with my collection and all the creations I made. As I entered my early teen years my collection had grown considerably and it was taking up a lot of space, and I was spending less and less time with Lego. I knew a younger kid down the block who was in the peak of his Lego phase and I donated my entire collection -- around five or so 30 gallon tras…
Or they can have a website where one can order a set and have a robot setup the kits from standard bricks. This should work for the majority of sets and would require a relatively small set of custom bricks.
Lego used to make custom pieces all the time. That, along with other missteps, nearly killed the company.
Product variety means changeovers (switching molds in the plastic injection molding machines). More quality problems will occur. Low volume parts for one set may use a tiny fraction of the mold's useful life, making the unit cost much higher than a 2x4 brick. You need more inventory to successfully fulfill any bulk order you receive. You also need to store the molds in an environment where they won't degrade over time.
Single Minute Exchange of Dies (SMED) and Economic Order Quantity (EOQ) work hand in hand dictating how to economically run a facility like this. EOQ considers storage costs, the fixed cost to setup the tool, demand per unit time, and time value of money to minimize the per-unit cost.
SMED reduces the fixed costs which are spread across a batch of pieces. This is the lever you can pull to reduce batch sizes, reduce inventory levels, reduce working capital, and help maximize profits.
To your specific comment, the difficulty lies in fulfillment. Making sure the robot picks up the right number of pieces which are unceremoniously ejected from the injection molder in no particular order. Having inventory of all the pieces people want - or having a relatively long lead time hoping you get enough demand to run batches on a make-to-order basis. SMED would make this a much more viable business model.
This article goes into more depth on the turnaround they went through.
https://www.theguardian.com/lifeandstyle/2017/jun/04/how-leg...
https://en.m.wikipedia.org/wiki/Single-minute_exchange_of_di...