Why is randomization important? And centralization likewise seems unimportant, as generating or sending a single auto-incrementing index number is really, reall

Why is randomization important? And centralization likewise seems unimportant, as generating or sending a single auto-incrementing index number is really, really fast. This is literally the technique I use at work for keeping track of part numbers: There's a single server that my individual CAD users can ask for a part number to describe the components of their assemblies, it does nothing but generate sequential, unique numbers. Engineers can't draw millions of parts per second, so it just works...and there's no probabilistic element with associated birthday paradox to the uniqueness of those IDs. There are only 4.5 people born per second for this hypothetical server to handle in the long term. And at INSERT speeds of something like 3M/second, you could theoretically handle the initial storm of requests to serve all current living humans in about an hour. With 2^64 records, this scheme should be good for about 100 billion years assuming population growth levels off. That's a long time for that assumption to hold true, but I think optimizing for an event that might be only 50 billion years away is a little premature (also, the timeout when querying this server from Alpha Centauri might limit your transaction rate, but again, premature optimization).