or they (game devs) were like: "shit...that left side border is annoying. let me try setting DIWSTRT earlier to compensate for the Amiga's hw bug" :) Other devs were like: "bah, whatever...I just want this project to end....it doesn't look so bad. just leave it be". which is why some games are centered and then some others are not.

I think it's a mixture of the original h/w "bug" and some devs trying to compensate for it while others didn't.

but, more to the point, i think the original "bug" may stem from commodore's hardware reference manual. they recommend Display window start and stop positions which are clearly not suited to most monitors. isn't that the actual problem here...rather than any hardware bug?

The only bug in the non-centered display is that the sprites are all fetched on the left side of the display instead of fetching half the sprites at the right side of the line before.

I still have my old 1438 monitor which I no longer use but it is still working, but it is fined tuned internally so that it is always centered when switching from native amiga AGA output & Graphics card.

WARNING HIGH VOLTAGE:

I found the setting on the right side of the monitor, look here & you will see 5 or 6 tiny holes where I can adjust the monitor settings, but i adjusted mine with the back cover off as its difficult to locate the adjustment with back cover on.

I used a isolated screwdriver (must be isolated due-to high voltage) inside monitor.

When switching screen between AGA & Graphics card it is always centred.

Default set-up is done by using the amiga boot menu, then switch to the same boot menu using graphics card display, no hardrive or floppy disk is loaded but private firmware in accelerator is required for graphics card to display output to monitor.

ALL MODIFICATION AT YOUR OWN RISK

That certainly would have been preferable but I think it wasn't done because it would have greatly complicated Agnus' DMA scheduler, unless one is willing to eliminate overscan completely.

Another way to center the display is to simply make it narrower, but proclaiming a 288 pixel wide screen would be embarrassing when put up against competitors that have 320 pixel wide screens.

But I agree with those that say the problem is a combination of Commodore docs recommending certain settings and programmers that didn't want to go through all the trouble of figuring out how to center things themselves.

Definitively confirm and remember this nostalgic issue with my 1081 (and others later) - a fine introduction to tweaking. It felt quite rewarding moving the picture around, mostly to the left. The stretch/width knob was never to be touched.

The prominent inclusion of the horizontal centering button by Commodore in the front panel of their monitors, indicates they knew this was an expected issue (or feature, from another point of view). A case of custom chips outclassing the monitors!

Toshiba TV
 

I got the same Toshiba TV as you, and the screen is pretty much centered when I use RGB to Scart. But when i use the Scart to HDMI, then it's just as your picture. In the menu of the TV you have an option to adjust the picture to the right or the left. I adjusted mine all the way to the left, and used the PC aspect on the TV. Then I get the full picture on the screen, but a bit right centered.

Because RGB often has a left shift on TVs. In this case it makes it centered then. :D

Weird. I was using SVideo at that moment, I don't have any HDMI converters.

CRT. Has vertical shift and horizontal shift been looked into on the input your using? Even H-EW, h-amp, v-amp, defection parameters. Maybe the TV is throwing the image data out of raster, newer TVs may be getting raster data that it does not handle properly.
I am aware of the issue and I think that the tuner on several televisions have a difficult time deciphering the image data and is very likely the image is not centered before the input.

Most televisions have a service mode, monitors that have no service mode need modification on the input or internally.

To me it appears like a half 4:3 chopped 16:9, I say the original format output is 4:3.

Is the impedance matched?