Really a best lubricant fit for each specific task exists based on the loads and needs, like grease for BB could be different than the one in the wheel hubs based on the different loads and speeds they reach (but it's not). But for a bike, loads are really low, (in comparative with real industrial bearings of same size like this light series bearing. You can see such a bearing outperforms the needs of a bike 1.3kN is a lot for one little 10mm bearing spinning at 80000rpm)

So in the end, does the type of grease matters? Yes but not here. Almost any type of grease would do the job fine and because of that there are a lot of bike companies who make their own grease (because any grease would do) adding price for "bike specific" and hype from the brand name.

Same thing goes for bearings themselves. Shimano is a nobody in making chains and bearings - this requires very high precision and special heat treatment, special finish on the raceway of bearings on the balls, etc. But since the loads are a bit on the low side they can make bearings fit for bike, not fit for a mining conveyor belt. They are not getting out the best of what a common bearing can do, but top bearing manufacturers do, like SKF, INA-F@G (that's the company name, auto-censor turned into ***), YABAN (for industrial chains - they make bike chains also but its no different than other bike specific chains) and others.

So my conclusion is that for bike specific products is a matter of taste and attachment to a brand name or consecrated recommendations on the forums. It really does not matter much. (and real stuff is expensive, sold by kilogram or even by barrel, and in a puzzling notation that fits best specific tasks like high speed, or high static loads, or dynamic shocks, etc and are in a gazillion types where it's hard to say what is fit without some engineering calculus)