I haven’t read the full thread, but here are my thoughts;
Losing the AI will make subsequent dives much harder, because knowing how much gas you have is pretty much mission critical.
Not knowing depth and time are things that would bother me because I like to know things like that. However, they are not essential for every dive. If you are going to have a hard bottom at 40 fsw, none of that really matters. As long as you know approximately what what your first was and whether you have any chance going into deco on the second dive, you can decide what is reasonable.
Err on the side of caution,
Should you have a back up DC? Are you okay sitting out the next dive because your computer failure beached you? If the answer is “no” then buy a backup, keep a battery in it and stick it in your BCD pocket. It doesn’t need to be identical to the one that died, it just needs to be on all the dives and you know how to use it. A decent used DC can be had on eBay for $50. If you are using AI, you will want to have and SPG somewhere at hand.
Some people go on their Sunday dive expeditions without so much as a spare o-ring. How much extra crap you bring along is entirely up to you.
How much you are willing to adjust your dive plan or spend on backup gear is also upto the individual. I know people who could outfit another entire diver from the trunk of their car.