That is not how real point of sale systems and stores operate in practice. I actually managed a retail chain of bike shops as the Buyer and back office manager. I was the one maintaining the point of sale connections and system. There are always errors in these systems largely due to new and incompetent sales staff that sell/return/enter duplicates of the wrong items. They can enter almost anything wrong, from gender to color, from model year to brand. I've seen them all.
Connecting these systems online is an absolute nightmare. I tried it with shopify, but had to limit the sku's to items I could completely control with minimal intervention from other staff. Generally speaking, the POS system in a local retail store can be more loosely managed where the staff can make up the gaps and mistakes when the POS system numbers do not perfectly match the local stock. If you want to track inventory like is required for online retail, you need a whole different kind of micromanagement and responsibility from staff. You also need something like quarterly inventory audits. These are quite time consuming and are a total loss in the labor time involved.
For online retail to be competitive, the margins with e-tail are absolutely untenable trash for brick and mortar retail. They are not even close. The biggest expenses are the commercial space rent and labor costs. With e-tail, the labor is less skilled, and the space is a cheap warehouse somewhere remote. General retail margins must be 40%+ while e-tail is 15-20%. The two are completely incompatible. This is why real quality brands do not sell e-tail. It has to do with how distribution and preseason wholesale buying works. There is more complexity to this, but overall the two are not compatible. In fact, most high quality brands will not allow most of their products to be listed online except under certain circumstances. This is to keep things fair to all parties and prevent undercutting based on whomever has the lowest overhead cost.
Selling online is only for low end junk and certain circumstances. If you are a high end consumer, you will likely understand this already. It is hard to produce high end goods and distribute them successfully. It takes local Buyers that know their niche market and can do massive preseason spending to collectively give the manufacturer an idea of what they need to produce at what scale. Otherwise, the business will not last long, or they must produce lower end and more reliable/limited products. This strategy will likewise fail due to over saturation of the market segment. It is far more complex than most people realize.