What does this daily test do? Why does it take 4mins? Is it something the unit can do keyed out, could it be set to do it when idle/remote/on a change over? Could it be speeded up? Is it something that could be done while the train is being cleaned/fuelled or otherwise idle?
Do the depots do it after every exam / train prep to at least get it out of the way for 27hours and so any detected faults can be fettled?
Do other units do it?
This test tests the functionality of the whole braking system, so it's about as important as things get on a train. On Northern's older units the equivalent test is done by the driver manually applying different brake 'steps' (pressures) and checking that the brake readings behave properly and do what's expected of them in each step. On most of Northern's fleet the braking system is an 'energise to release' Westcode 'three step' system where braking positions relate to semi-fixed braking efforts. Positions are release, step 1, step 2, step 3 (aka full service) and emergency (brake control wires earthed so that the energise-to-release aspect is failsafe).
Edit 2: on the CAF stock the brake is a different system, is computer controlled rather than electro-pneumatic and is continuously variable rather than 'stepped' all of which add a complicating factor for an equivalent brake test.
The test takes four minutes because it does. We aren't furnished with the technical details, but the brake test applies varied pressure to each axle in turn (while keeping enough brakes applied in a controlled way to avoid any gravity related issues) in a way that tests the application and release of the whole system throughout the train, and presumably verifies the communication signals passed amongst the systems responsible for brake control. It takes four minutes regardless of whether it's a two car set or a twelve car lash-up - any coupled units can be set from one cab on the whole train to perform their brake test simultaneously.
It can't be done while keyed out/idle/remote or on a crew changeover because the unit is hardwired in a way that makes that impossible, no drivers desk on causes an emergency brake application for obvious reasons. Any door open or released causes emergency brake application. This will not be changed. You'd need to read the various group standards documents available from the RSSB for the technical reasons why all trains are designed this way.
Could it be sped up? Probably, but not significantly, and will no doubt cost money. Faster/cheaper/more reliable - pick two.
Whilst cleaned/fuelled/otherwise idle? Possibly, but the brake test would still need carrying out as part of a full prep procedure because it is a vital part of that procedure, the full prep is the most appropriate time to carry it out because there is documented evidence of when full preps were carried out, and they are more likely to be carried out reasonably soon before a unit is due to come in to service. If a unit arrived on a depot on a Saturday night at 0200, it was cleaned and fuelled an hour later and the brake test carried out while being cleaned/fuelled rather than on full prep. There would have to be a separate procedure instigated for recording the carrying out of the brake test in isolation outside of a full prep, and even then let's say that unit isn't going to be due off the depot til 0400 Monday morning, after a full prep but without a brake test. An hour after it comes on to the main line, it is going to need a brake test.
Edit - I should add that there would not usually be a driver present while the unit is being cleaned, fuelled or idle - so you'd be adding workload and therefore needing more drivers.
When a full prep is carried out the documented evidence of that unit being prepped is only valid for a limited period of time, after which the unit needs prepping again.
The ORR would be very interested in any TOC/FOC whose safety case didn't require testing brakes as part of a full prep procedure before venturing on to the national network.
Do other units do it? Yes, a lot of new traction units are the same.