I don't know what properties you think people are trying to pragmatically prove about arbitrary programs but "did the program complete successfully" will always be an important, pragmatic property in software development. Especially in the pragmatic world where so much of our software is chaining smaller programs together to solve a task.
I'm saying we can't write perfectly bug-free software because of the Halting Problem and the inability to prove any given loop will not be infinite until running that loop. Perfect remains the enemy of the good and we certainly write a lot of "bug-free-enough" software without worrying about the Halting Problem day-to-day. But if you are saying the world needs to write perfectly bug free code starting tomorrow because LLMs will find all the vulnerabilities and sandbox escapes the Halting Problem is absolutely one of the reasons we can't ever provably hit that "perfect" target. We still need to find "good enough" or we give up on software development altogether and that's not what I'm advocating. Perfect is the enemy of the good. Mathematically perfect provably does not exist. Software will always have bugs, especially in the world with a threat model of active brute force machines.
If you sacrifice precise and widen it to: "Halt" and "Maybe run forever, but might just take longer than the age of the universe and is thus irrelevant for actual programs we might choose to run" then it is decidable for every problem.
Every means that there exist programs, in the infinity of all programs, that can not be proven. It does not mean that no program can be proven. Programs that are 10^8000000 instructions long that are intentionally obfuscated count in every. Human-designed programs that humans want to be correct and are reasonably sure are correct are extremely well-behaved in comparison and their provable termination can almost always be reasoned about.
Generally speaking, human-designed programs are almost always implicitly being constructed in the space of programs that will terminate (possibly relative to a event loop). At every step of the process you only extend using provably terminating constructions. Few humans will have a loop condition like: "Terminates if the Goldbach Conjecture is true" which is one of those sorts of things that makes it hard to prove termination. Just stay away from unproven conjectures in your loop conditions and you will probably be fine.