Who do you think gets all the business on competing routes? Filling even 5% more seats on average dramatically improves airlines P&L statements.
I'm not saying it's rational, but big businesses have been built on the inability of the average person to do math. (Airport insurance kiosks, lotteries, pachinko parlors, or Las Vegas/Macao.)
(I'm also not suggesting that there's an easy way to get that 1 in 200 improvement in safety, even at a 10% cost penalty, but if your airline gets a reputation for bad safety, you're all but done, even if you come up on the top of Expedia/Travelocity/ITA searches when sorted by price...)
LOTS of very useful things will kill far more people this year than commercial air travel. Water buckets. Bicycles. Doctors. Cars, in about the first two hours of the year.
(If you took a Boeing 747 full of American patients to a doctor's office, more than one would die due to medical error. Remember that checklists article from yesterday?)
Air travel gets the evil eye because the deaths are very visible. The same factor would make market-regulated air travel very safe.
If you don't use checklists, your premium next year will triple."
There's a tipping point for "dangerous airline". 0.5% more dangerous than any of the current airlines wouldn't be noticeably less safe (i.e. 20 vs. 21 crashes for an airline) and if they were competing on costs, the cheaper one would win. And if somehow one airline, despite only a 0.5% difference in safety gap did get branded that way and the rules remained the same, there'd be a market gap in there for a new airline with the same bad standards to come in and fill.
All an individual cares about is 1 vs 0 crashes-per-flight, not 200 vs 201 crashes per bajillion flights. So if I could buy a ticket on Qantas (0 fatalities in their entire jet era) or Aeroflot (31 in the last 19 years, including 2 unrelated on the same day from the same airport) for the same trip, I'll clearly take Qantas, even if the Qantas flight is 3x as expensive, as I assume most people would.
But here's where humans don't do math well comes in. Even a tiny difference in actual safety is dramatically over-valued. "No child of mine is going to be subjected to an extra 0.5% risk just to see some big mouse in Florida! I'd sooner drive there than fly THAT airline!" And that is how airlines with a bad reputation for safety end up merging, getting bought, shutting down or simply changing names. And how people who can't rationally make decisions end up driving 800 miles to Disney instead of flying, because the risks of driving are much less visible to them.
This might be less true of those who don't fly often for whom it's a big deal, but I'd guesstimate business travelers care less.
If you say to Joe Public "this airline is 0.5% more likely to have a crash than the one that's $50 less; which one do you want your family to fly?", I doubt many people can easily say "Oh, the cheaper one is preferable." They may arrive there after some agony, but to instinctively know that an extra 1 in 200 on something that's already 1 in 3 million or so is not economically justified on an EV basis. (You'd have to value your life at $30 billion dollars for there to be an EV equivalence between those two choices.)
Nonetheless, I predict many more people would find ease in deciding to take "the safer, more expensive airline" than would find ease in taking "the less safe, but cheaper airline" for their family travel.
You would want them to be selectable (engaged during low-altitude flight, stowed during cruise flight) so as to hopefully not unduly hurt range, other than via the increased weight.
The problem though is that there are significant one-engine-out climb performance targets that must be met for Part 21 certification, and inertial separators have power penalties on top of the weight penalty. Taking performance away from a one-engine-out scenario would further restrict max take-off weights, increase balanced field lengths (meaning some airports would need to make improvements to serve some aircraft, etc), increase the time from roll to V1 (the takeoff commit speed) and at the end of the day, taking performance away may represent a higher risk than birds currently represent.
In 700 hours or so of single-engine piston flight, I've struck two (small) birds, and had close calls with half-dozen more. I've never had a close call with a bird over 2000 feet AGL, so cruise flight could surely be done without brid protection.