My system photo library showing on all my Macs

Yes, that is exactly how it works. The System Library on each Mac is the only one used for iCloud which will be available on all devices. You can open a different Photo Library on the Mac and those photos will not be synced to iCloud. If you designate that Photo Library as your System Photo Library, then any photos there will be merged with those in iCloud and once again all photos will be the same across all devices. There is only 1 Photo Library in iCloud and that is the System Photo Library.

Designate a System Photo Library in Photos - Apple Support

The System Library is the one that other apps on the Mac can use-- it's the one that Safari goes to, for instance, when you do an upload or download. The System Library is also the only Library that connects to iCloud. While Macs can have more than one Library, there an be only one System Library. iCloud, iPhones, and iPads have only one Library, so there's no need to designate them as the System Libraries.

The System Library on each device is really a separate entity, and even if you do choose Optimize, you are always looking at pictures that are on the device. Photos doesn't show pictures from the internet. It shows pictures stored in its Library. If Optimize is used, then smaller resolution images are kept local, and those are the ones you use--until you go into Edit mode where larger images are downloaded from iCloud.com.

One of the disadvantages of Optimize is that you can't back up files that aren't there. So it's important, if you can, to have one Mac Download Originals, and to regularly back that Mac up with something like Time Machine.

So--you're doing fine!

Stephen Schulte1 wrote:

In the Photos App on each Mac when I open my "main" photolibrary and go to "Settings" the "Use as System Photo Library" is greyed-out meaning that each of the 3 macs has its own "System Photo Library". IS THAT HOW IT SHOULD BE?

It's greyed-out to tell you that you have already selected that library as the System Photo Library. There's no need to go into LIBRARY A which is the System Photo Library and change it to be the System Photo Library again. If you went into LIBRARY B, the control would be available because using it would actually do something.

If you are using iCloud Photos on all three Macs, under the same Apple ID, then each of the Macs will be attempting to keep its local System Photo Library in sync with iCloud Photos. By this means, the Macs will indirectly sync with each other, and with your iPhone.