What if both wheels were powered by pedalling? Only the rear wheel of a bike is connected to the drivetrain in order to propel the bike forward. I assume the choice of rear wheel instead of the front wheel is for stability (e.g. avoiding 'fishtailing' and other problems).
However, would there be any potential benefits if, somehow, both wheels were connected to the crankset so that the input power could be shared between the wheels? (This hypothetical system need not use a chain – c.f. shaft-driven drivetrains like CeramicSpeed.)
One advantage of a two-wheel drive system is that there could be improved grip and control on uneven, off-road terrain but the disadvantages probably outweigh this benefit.
The obvious disadvantage is you would be powering two wheels instead of one (so the rotational inertia would double?). You would also have to deal with the fact that you have to steer with the front wheel too!
I doubt any sort of bike like this has been made* / will be made in the future, but it's interesting nonetheless to imagine what this could be like...
*EDIT: As the comments have pointed out, they do actually exist.
Many two wheel drive mountain bikes exist. Here's one article advertising a new one:

There’s been no shortage of attempts to build a workable two wheel
drive bicycle over the years, but this latest effort from Double of
Japan looks like one of the most compelling yet.

https://www.bikeradar.com/news/this-is-a-two-wheel-drive-bike-done-right-sort-of/
They do offer better traction in some situations but I've never seen one with a limited slip differential between front and rear, which means they need a freewheel for each wheel to avoid stressing the drivetrain (you really don't want one wheel pushing backwards!). The extra weight and drivetrain complexity is always there but the extra traction is only useful very occasionally.
The other problem chain driven ones have is limited steering range (see the one in the article above). That's not a problem on FWD speedbikes where the steering range is limited by the fairing (often to +/- 5 degrees or so), but for technical mountain biking it's a huge issue. I commonly steer +/- 90 degrees in technical sections, and even on normal trail climbs half that. But getting a +/-45 degree swing out of a universal or CV joint is hard to impossible.
There are also flexible cable drives. Those trade more steering movement for more losses and generally shorter service life (ie, the only one I tried broke, luckily not when I was riding it). With a flexible shaft some wind-up is actually useful, as it gives a bounce in the drive to help you over large bumps. But it's disconcerting when riding and overall burns effort from the rider to counter the wind-up all the time while helping occasionally.
A rigid shaft drive could in theory have a rotating linkage with 180 degrees of steering freedom, but would be quite complex to build. It would also need a telescoping section if there was front suspension, and likely significant gearing to reduce the shaft size (and the torque on the sliding section as well as on the steering).