Looking at this from a business point of view, I suspect "Patch Tuesday" was started so that Sys admins could actually set aside some time in their potentially busy schedules so that they could test patches both adequately and quickly.
You say that business can and should be implementing their own patch schedule. They should, but when Patch Tuesday started, Microsoft did not offer a coherent way for ANYONE to do this, and only started offering them two years later. Even now, they only offer a way to do this if you have a Windows Server available on the network. Something which is not cheap, and may not be feasible for small businesses, who may have a few PCs but don't have someone they can dedicate to running a server.
For these people, there may also be the problem of link usage. If they know that all their PCs are going to be using the link to the internet at a given time on a given day, they can schedule anything time sensitive (such as IP based telephone calls) so it does not happen at that time. They can, if they are savvy, also set up their PCs so that they power up at this time, thus enabling the company to save power (and therefore money). OK, so Windows Update will check when the PC is powered up anyway, but this might still cause problems with Link use..
I think Microsoft are going about this the right way. Consumer get the updates whenever they are released, but businesses have a set schedule that they can use. I suspect Microsoft have been a bit slow to introduce this because it is quite a massive change for Windows Update, and if it goes wrong, the effects will be felt world wide. I also suspect that they introduced the fast and slow tracks in Windows Update on windows 10 to test the backend changes required (the Consumer edition being the fast track, and the Business edition being the slow).