RAT5, I do not agree with you on this I am afraid.
When CDA is mandatory at destination, the use of VNAV PTH can be very useful when being vectored around, provided the FMC reflects accurately what you are planning to do, update as you go around the lateral profile to keep you flying a CDA.
Some 737 are fitted with FMC logic enabling this, geometric descent path approach, so use it properly. Maybe you have not been in a position to fly one of them yet, as I have been with operators that have not in past or in deed current operator prior to adjusting the setup cross-fleet, it is worth it for sure.
As you stated: "Why were the expected prompts not available? Afraid I can't answer that one". I tried to answer this for the benefit of the OP:
FCOM 2, Flight Management, Navigation - Flight Management System Operation:
"In approach phase during speed intervention, the pitch mode remains in VNAV PTH after speed intervention is exited. The FMC shall remain in the current vertical mode regardless of IAS MACH selector changes."
"The following situations are generally encountered during approach operations, but are not determined by “on approach” logic:
If speed intervention is engaged:
• during a path descent with flaps up on an idle or non-idle leg, VNAV switches to VNAV SPD
• with flaps down, VNAV remains in VNAV PTH
• "on approach" with the MCP Altitude set greater than 250 feet above the current altitude, VNAV remains in VNAV PTH
• when a point to point (geometric path) leg is active, VNAV remains in VNAV PTH
• while a vertical angle leg (GPx.xx on RTE LEGS page) is active, VNAV remains in VNAV PTH
• if a vertical angle leg (GPx.xx on RTE LEGS page) becomes active, VNAV switches to VNAV PTH without pilot action
• if on a vertical angle leg, and cross track exceeds two times the RNP value, while LNAV is not engaged, VNAV will disengage."
Plenty of reasons in which VANV remains in VANV PTH, any of those could have happened to the OP...