What if backward compatibility had remained the standard on post-Crash consoles?

[Gameguy]

Similarly, the Dreamcast skipped Saturn backward compatibility as well.

And we could see how well the Dreamcast sold, compared to the PS2 with both PS1 and DVD compatibility. To be fair, you could still play PS1 games on the Dreamcast using Bleemcast and use a PS1 controller with an adapter, though by that point it would just make more sense to buy a PS2 and also enjoy DVDs. And enjoy PS2 games, which were better than 99% of all Dreamcast games.

The PS1 wasn't backwards compatible with an earlier console, but it did have a built in CD player which convinced plenty of people to upgrade to this console. Basically a console being multipurpose is what helps sell it, not just with backwards compatibility. Lots of people at that time didn't have CD players yet, it was a big deal when it launched. Plus there were accessories that let you play VCDs on the console which could be appealing as well, though not necessarily in North America.

With the NES, not having any predecessor was a benefit at that time. Nintendo avoided marketing it as a video game console because people avoided those due to the crash, adding backwards compatibility would have associated it with an earlier console that people would want to avoid at this point. Nintendo was a success at that specific time because it was viewed as something completely new, it wasn't seen as just an updated video game console with cartridges like a newer Atari, it was a completely new home entertainment system using Game Paks and had a robot.

As for the SNES, it was originally supposed to be backwards compatible with NES games but that feature was dropped to lower console costs. There was a 3rd party adapter that accomplished the same thing, though it's pretty rare to find. At least the SNES did get the Super GameBoy to play that library on the console, not at launch but it might have helped with later adopters who already had a larger Gameboy library.

That said, with Nintendo portables backwards compatibility was usually kept as a selling feature. The Gameboy Color and later the Gameboy Advance were backwards compatible with earlier cartridges, then the DS was compatible with Gameboy Advance games, and the 3DS was compatible with original DS games.

In regards to your main question the N64 and Saturn probably would have sold better if they had backwards compatibility assuming the console costs would remain the same, though the N64 didn't exactly sell poorly overall. The Saturn would have sold better if it was fully backwards compatible with at least the Sega CD, though much better if it was fully backwards compatible with the Genesis and 32X. At least with the Sega CD weren't those games on clearance when the Saturn was out? If so those would have been an easy cheap library for people who never spent the money on Sega CD hardware previously, personally I'd find that enticing while waiting for the latest and greatest new Saturn games to come out, all this before people were burnt out on trusting Sega hardware. The biggest reason that affected the sales were the competition, if the competition wasn't so good then the Saturn would have done better even without backwards compatibility. Not sure about the Dreamcast though, people were burnt by the Saturn so few people trusted Sega by that point, plus the competition with the PS2 was just too good, that and Dreamcast games and controllers mostly sucked in general. I'm sure if the Dreamcast had much better games then it would have sold better too before the PS2 launched.

The Power Base Convertor is technically compatible with the Model 2. It just does not physically fit the console without either modifying or removing the adapter plastic housing.

You can use a bridge type adapter too instead of modifying the adapter, like an early import converter cartridge that doesn't deal with actual region lockout. It raises the Power Base Convertor above the console so the shape isn't a problem anymore. There's also a Master System Converter II available in other regions that does fit with a Model 2 Genesis/Mega Drive. It just wasn't sold in our region as Master System Games didn't sell that well here so few people would have needed or wanted it.

As for your other point with limiting hardware to old specifications, that's both yes and no. Instead of just sticking with using an old sound chip, they could have had 2 separate sound chips. Lots of backwards compatible consoles do this, they'll have both a new and old set of chips to play both types of games. This does free up the issue with limiting hardware, but doing this adds to the console cost and companies often decide that lowering the price is overall better for business than offering backwards compatibility.