Shimano’s Words
Looking at the Shimano bleeding guide, it is pretty comprehensive. It’s basically a back-bleed using a syringe into an upper catch tank (the “funnel”), followed by a gravity bleed into a bag, followed by a ‘conventional’ pressure bleed of the caliper using the lever/master as the pressure source, followed by a final reverse gravity bleed of the reservoir, and a neat clean removal of the catch tank.
You can do all of this without the funnel, but it won’t be as clean.
In most hydraulic breaking systems it isn’t so important to get all of the air out of the reservoir – every road car / road motorbike reservoir has air in it (at the top). For this application though, where excessive vibration could lead to any air in teh reservoir getting mixed with the fluid, then introduced into the pressure line it is desirable to get all of the air out eventually during the bleed.
You could do all of this with just a large syringe though, and some rags to clean up any overspill.