They were seemingly a favourite of the Mersey Railway, and the line to James Street was fitted before the loop and link schemes. When the loop line was constructed they continued with the same and only practical method of train protection.
As part of the construction of the link and loop, the Northern Line stock was fitted with trainstops to allow interoperability, and the Mersey stock modified to work with the BRB standard design.
All signals in the link and loop, and on the approach, were fitted with tripcocks. The number proposed was 50 - how that stacked up in the end I don’t know.
I suppose the rationale behind keeping the tripcocks in the scheme was the relatively unique metro style signalling system and the whole risk from tunnels. Certainly in the loop most of the signals do not have a yellow aspect. The sighting distance is the braking distance, and the tripcock has to guarantee the train stops in the overlap.
Two sidings were fitted with “Tooting” controls halfway down the sidings at James Street and Liverpool Central. These were set to lower on a timer after track circuit occupation, which was based off of the maximum permissible speed.
More generally there was a document released under a FOI request for the loop & link working instructions which has details on trip cocks, found here:
https://files.whatdotheyknow.com/request/merseyrail_drayton_park_dc_instr/NR_L3_ELP_27051_MANUAL (003)_redacted.pdf