For that to function as an answer for the Big Silence it can't just be something that can happen, it has to be something that happens virtually all the time. Think about the various absolute (reasonable) worst case scenarios for us. Fossil Fuels run out and we kill each other off in a cannibalistic orgy? Doesn't really work, there's a population density you drop to where there stops being any advantage to attacking even if you haven't got ethics. If you're down to about 50 million people, less than 1%, you've got about 1 person per mile. People might not universally return to peaceful cooperation and trade, but you'd basically be back to a scale where light agriculture and HG were doable, with lots of ruined and/or repairable tech around to serve as models or scrap for melting down, it wouldn't take that long for the population to crawl its way back up into the billions having learned whatever lesson it needed.

Even in some more extreme doomsday than 99% dead, one little island haven or remote fortress of 1000 people could repopulate the planet in a millennium or so, 50 generations of even molasses slow growth can take 100 to 1 billion, twenty generations of doubling would do it and people can do better than double a generation if they need to, but even if the average couple only had 3 kids that reached maturity we'd be back up to normal pop in around 700 years and odds are the planet would have recovered from whatever was done to it. You really probably only need a few tens of millions of people to support a modern tech culture. A millennium is a small time on this sort of scale.

Species wiping themselves out certainly can't be ruled out, but for it to be an answer to why the space is so empty it has to be something that would occur so often and inevitably that at a very minimum the species it happens to must be orders of magnitude higher than those it doesn't happen to, and we're talking total wipe out not 'temporary' century long crashes, and that wouldn't appear to be the case. Now, something like 'nanotech machines run wild and render entire ecosystem, from people to blades of grass to the dirt they grow in, down for scrap in their gray goo' might do it, as could something like easy production and storage of anti-matter, but even then - and assuming those are options - the presumed inevitably comes form the idea that a single lone maniac could wreak ultimate ruin on his world in his garage and that a species is bound to have a few clever madmen. That sort of thing requires us to assume a tech can be developed and that no control factors could exist to limit the doom caused by reckless or wicked loners or small groups.

However, even these sorts of Technological Singularity Doomsday scenarios don't really explain the silence. Consider, if you have anti-matter production at that scale, then you have spaceships capable of interstellar travel. No ifs, ands, or buts about it, and more importantly you have a power source that can broadcast the "What's up aliens?" signal very, very loud, and the same applies to any sort of nanotech like that, where a pen-sized rocket full of droids can crash on any planet and terraform it and clone plants, animals, and people to inhabit in decades to centuries from launch, especially if you've got both AM and NT available, which gives them easy species survivability options that pre-date or parallel the doomsday option. Which isn't a necessity anyway because the conundrum of the silence isn't avoided by dead species, it's only avoided by species averaging a broadcast time/strength smaller than that which is required to explain our own lack of reception during the interval and sensitivity we've been listening with. If a million species evolve to broadcast level over a million years in this galaxy, and each broadcasts loud enough for us to hear for a century on average, we should be receiving 100 signals at any time... and that further assumes someone doesn't do something fairly obvious like use automated transmitters with long term power sources.

I don't think inevitable species destruction can be considered a valid explanation for the silence, even if you start going for more murky vanishing options like 'went to another universe' or 'turned entire population into software-people living in a simulated reality' some of them would presumably kick around, or at least leave a transmitter behind saying "Yo, have found way to travel to new cool universes, it's done like this" or "Please be aware that while we're all virtual critters now, if you come near our computer core we will blow your fleet into smithereens, be smart and follow our path, throw off the material!" and so on. True they hit the 'blaze of glory' option followed by staying at home to live small, but only kinda sorta, nothing would stop them from running a transmitter saying "Yo, Howdy" while otherwise being relaxed and small societies, just a culture that is either unable or disinclined to stop one dude from setting up a transmitter as a hobby.