Strength of balsa wood vs. strength of steel

And historically could. de Havilland Mosquito - Wikipedia

Of course, the real problem with building structures out of balsa wood is that you’d be inundated by zombie Cub Scouts.

when a wooden boom had enough strength it might be too big and heavy to use.

Might be able to make bearings out of wood, but it’ll be a lot more intensive hand work.
Very applicable to shovels, but also as a more general point: one of the great things about metal is not just its strengths (plural, since there are a bunch of different kinds), but the way it fails. When metal is loaded past its strength, it starts bending. With only a little overload, you get only a little bending, so the structure probably stays together, and you might be able to repair things just by bending the metal back. Wood, on the other hand, tends to splinter, which will lead to concentrating loads and complete structural failure.
So even if you had a wood as strong as steel, it would be a bad choice for a shovel. Think about all the tiny little dents and dings from hitting rocks that a used steel shovel has. With a wood shovel, a tiny ding could cause the whole shovel to split.

Yup. This is why miracle glues won’t help make a backhoe bucket out of wood, unless the walls of the bucket become too thick to be practical. But the rest of the backhoe is basically beams. Wood bearings would just have to be much larger, and a corresponding increase in size in the beams at the bearing location. I haven’t looked it up yet, but I think the cost of building the backhoe in oak or similar hardwood would exceed the price of steel these days. But it would be more fun to do.