>>Random distribution seems like it would be better for write performance - it means that inserting multiple new values and rebuilding the index can happen in parallel rather than having to coordinate the auto increments. It also naturally has the right properties for sharding as and when you get to the point of needing that.<<
I'm not sure what you mean by "inserting new values and rebuilding the index can happen in parallel." In most storage engines using clustered indexes, writes that append to a b-tree are faster than writes that insert somewhere in the middle of a b-tree so there really isn't any rebuilding of the index required in the former case.
>>On the read side it shouldn't make any difference, as there's no reason the rows you want to access at any given point should have any correlation to when those rows were created.<<
That depends entirely on the nature of your workload. There are plenty of common workloads such as sensor data or log entries for which the common read patterns are very much correlated with the order in which the rows were written.