It all helps. Even for open-coil pickups it will block interference coming from behind and to the sides the guitar. And as on stage you normally stand with your back to the amps, then it should cut out any hum from those.

The size of the gaps in your 'cage' determines how effective the shielding is and the wavelengths it will keep out. Any wavelengths smaller than the gap will get in, but any waves longer than the gap size will start to be attenuated as the wavelength increases. With the wavelength 10x the gap size, almost all has been attenuated and at 100x the gap size, attenuation is to all intents and purposes infinite. So even with an open-topped box like a pickup cavity, with say a 5cm longest side, you are effectively blocking all interference that has a wavelength greater than 50cm, so effectively blocking up to at least 600MHz.

Microwave ovens have a grounded metal grid on the door with holes big enough to see through, but they are small enough to block the cm wavelength microwaves used from getting out and cooking you!

Of course not all of an uncovered pickup is inside the box, so it's not perfect, but it does help.

If you fit a covered pickup and the gap between the grounded cover and grounded shielding is say 0.5cm at most, then you're protecting it up to around 6GHz.

The pickup is the bit with the most length of wire on it, so it makes sense to try and shield the pickup as much as possible. The shorter lengths of wire used in the control wiring harness are less prone to picking up noise, but the longer they are the more noise they are likely to pick up, so with a strong source on interference nearby, they can pickup enough noise to be audible, so it's worth shielding the control cavity and using screened cables that run outside the cavity where possible.

As an aside, most '50Hz' or '60Hz hum' you hear on a guitar or bass amp is actually 100Hz or 120Hz hum (plus higher harmonics), especially on valve amps.

50/60Hz is a much lower frequency than you normally hear as hum'. Here's an online tone generator, you can use for a simple comparison in tone. https://www.szynalski.com/tone-generator/

50/60Hz is the mains electricity frequency, and it's what you may pick up from the mains transformer as magnetically induced interference, but most hum is higher pitched and comes after the mains is rectified. You then get positive ripples on the DC supply with 100/120Hz frequency and unless you are very close to the amp, it's this that gets radiated and picked up.