( I think the introduction of colors and sound to cheap( 1980 onwards
) home-computers from 1975 to 1985 was the reason( or a reason ) why
they were so slow or incapable of satisfactorily displaying 3D moving
graphics, and yet this was the sort of effect for which many people
bought the machines, I have always wondered if there was a secret
'Monochrome-Mode' available in many of these machines from 1975 to
No, no, and no.
The demand wasn't there
Back then few people bought home computers for 3D graphics. 3D was used mostly in high CAD workstations, which were very expensive and not optimized for arcade games. If the demand for 3D was higher then manufacturers could have optimized their chipsets for it. But most people wanted fast 2D color graphics, which is why chips such as the VIC-II and TMS9918 were developed.
Even after 1985 most home computers concentrated on producing good 2D graphics. The Amiga was the ultimate example. It had a hardware blitter which could draw lines, and the AGA chipset could produce 256 colors. But screens were built from multiple monochrome bitplanes, and the blitter (or CPU) could only work on one bitplane at a time. This was ideal for scrolling 2D backgrounds etc., but not so good for 3D graphics.
The only 80's machine I can think of that was designed specifically for 3D was the Vectrex video game system. It used true vector graphics (not bitmapped, the CRT beam was moved directly around the screen to draw lines) with plastic screen overlays to simulate color and static graphics. The main problem with this design was poor text and zero bitmap capability. It didn't last long and was a commercial failure.
Proper 3D graphics didn't become popular until the IBM VGA card became a standard. It had a 'chunky' 256 color graphics mode with 1 byte per pixel which made mapping surface textures easier. Games such as Wolfenstein 3D and Doom changed people's desires. But it wasn't just the VGA card's chunky pixels that made these games work. They also needed lots of memory and a powerful CPU, things that were beyond the reach of home computers in the early 80's.
The CPU was the bottleneck
Colors could be reduced to speed up rendering. Sound was usually produced by independent hardware, or by toggling a bit in-between doing other stuff. But RAM was slow and expensive, and the CPUs were relatively inefficient.
Without a floating point unit or even integer multiply/divide instructions, the CPU spends most of its time doing calculations. Setting pixels is just the final stage and only takes a few cycles. This is proven by the fact that true 3D games were much slower than complex 2D games, even on machines that had no hardware scrolling or sprites. Games that used pseudo 3D techniques (eg. isometric 3D, scaled software sprites, multi-layer backgrounds) could be just as fast as 2D.
Any 'secrets' were soon discovered
Most machines at that time had monochrome graphics modes that were no secret, but color was more desired for games so the monochrome modes were used less. Some machines (eg. the Apple-II) were both mono and color at the same time, depending on what screen they were hooked up to. A few machines did have 'secret' graphic modes that were simply unintended side-effects of how their chipsets worked - most of them not particularly useful and perhaps even dangerous (eg. reprogramming the sync timing on a 6845 could blow up your monitor).
I'm thinking that a single-color-monochrome computer by default, would
be faster than one which has single-color-monochrome only as a
selectable mode( since the color capability would still be present etc
No. The designers of these computers were acutely aware of the limitations and trade-offs that had to be made to get the best performance at lowest cost. Creating a screen mode that doesn't use color but suffers the slowdown of having it would be stupid.
The main reasons for color slowdown are that the CPU has to write to more memory and/or the display controller steals more bandwidth. At the same resolution in monochrome mode the CPU has less work to do and bandwidth requirements are lower, so it can render faster.
Some machines allocate the same amount of video memory no matter what the graphics mode. Resolution then increases as the number of colors decrease, negating the primary benefits of monochrome. However that doesn't make them any slower than a purely monochrome machine at the same resolution.