The other tension in any safety system is that any time the safety malfunctions by not releasing when it should, you’ve created a dud. So as much as you want the entire bomb to fail by failing safe, you want each of the redundant safety systems to fail by failing hot.
The enemy will not give you a do-over or laugh off a dud arriving at one of their vital facilities.
There was an issue with a safety system on the early model Polaris SLBM which rendered almost the entire inventory duds. Which defect was not discovered until after a few years of patrolling the seas with them, intending the threaten 2nd strike doom upon the USSR.
As to the OP’s specific question, the answer is simply that these devices were much simpler than what you’re imagining.
As a 100% made-up example: It’s easy to build a barometer-like device which closes a microswitch at a given pressure. And to connect that to a latching relay so once the switch closes a circuit stays in that new state forever. Install two such barometers set for, say, the pressure at 25,000’ and 15,000’ ft. Then build a simple circuit out of some relays & a timer that requires the following events in sequence:
An arming switch closes when the bomb leaves the airplane (or more precisely, when a wire is pulled out of a connector on the exterior of the bomb).
The 25,000’ barometer fires. which starts a timer which runs for a few seconds.
The 15,000’ barometer fires BEFORE the timer runs out. The time interval is chosen to be just a little longer than the time of freefall from 25,000’ to 15,000’.
Bottom line: For a half-dozen relays, 2 barometers, and a timer, you’ve got a mechanism which ensures the bomb got dropped from above 25,000 ft.
Remember these bombs were big, like the size of small passenger cars. And incredibly expensive. So that means there was plenty of physical space for however much 1950’s electronics they needed and batteries to power them. And cost of the fuzing & safety mechanisms is/was immaterial to the total cost of the weapon.
To my mind the truly hard part of these kinds of designs is building them to be tamper-proof or at least highly tamper-resistant. If the bad guys stole a bomb, they could tinker with the safing mechanisms at their leisure until they figured out how they work and how to bypass, remove, or fool them.
Kinda like protecting your laptop data from assault over the internet is very different from protecting it from a techie bad guy who’s stolen it and has your hard drive laying naked on his workbench.