I always presumed that those kinds of experiments existed or were done in the past, there is after all a fair amount of knowledge about the relays, but they were discontinued when they stopped producing results or the races lacked the technological advancement of some one like the Protheans, needed to advance the research. Similar to how I view the species reactions towards the Keepers, the Asari and Salarians probably ran research on them thousands of years ago but when they discovered nothing they discontinued it and wrote the law requiring people to leave them alone.
But that's not how human's work. I can't speak for the aliens, and humanity hasn't been on the galactic scene for very long, but there's got to be at least a dozen human's going absolutely NUTS about not understanding them fully, dedicating their whole being to try and solve it.
Now if only human's work like that then there's some room in the game for the technology not being fully understood yet. But if the aliens work the same way (and I deem this very likely), there have been legions of organics going absolutely nuts about not understanding it yet for millenia. They would never stop. They would die not understanding maybe, but there'd always be groups of people trying.
We never see this in the game, it's not even spoken of.
Same goes for the keeper law... has always baffled me, from the very first time I played the game. Now matter how impressed I was with what I saw. (can you remember the first time you got on the Citadel, and how immensely awesome that felt? That's where I fell in love with ME)
Why would you NOT research them? They are tending to your home, your seat of government. You'd want to understand that.