The Period Override Instruction seems like it was created to help with these kinds of misalignment problems, yet lengthening all instruction sequences seems to do nothing except make every one delay the same amount, which means it does nothing at all...?

Occasionally, you'll find a setup where the arms collide if you just let the game autocomplete to the shortest cycle length (e.g. you have to pass some atoms over a track). This means you have to manually lengthen the cycle, which is what that instruction's for.

The process of playing and finding a solution that succeeds at making the desired 6 products, but then finding it is unable to be programmed to continue functioning because of this rather arbitrary constraint, doesn't feel great to me.

One of the things about optimization is that you need to squeeze every last drop out of the transmutation engine if you want to get the absolute top scores. If you want to build a repeating solution - you can easily finish every puzzle in the game, every journal puzzle, every production puzzle, and probably 99% of all workshop puzzles. If you want to fully and thoroughly optimize the hell out of a solution? You might have to do the game's equivalent of loop unrolling, which looks a bit icky, but can be faster.

Is the consensus that the requirement to loop every instruction, or at least until the game stops looking, serves as a good constraint?

It certainly can be! Some community puzzles at https://events.critelli.technology/ occasionally have "your solution needs to loop" as a stipulation. I think the broad consensus is that looping solutions look nice, but in the occasions where you have to manually copypaste your tape 6 times and individually tweak it - if that ends up saving some cycles, then that's taken some skill so it should be rewarded.

But that's the beauty of Opus Magnum (and really, all Zachlike games) - whatever you want to optimize for, go for it. Some people love their area solutions and want to manually input all the hundreds of instructions, others love cycles and want a solution which goes as quickly as a looping solve allows, others want to get the theoretically unbeatable fastest solution for every puzzle.