I do not believe that “slightly better avionics will completely avoid the vast majority of GA accidents.”
You will see accident reports where the problem is that the pilot just completely failed to put enough fuel in the airplane and then flew it until it ran out; but that's not the typical thing.
What's much more common is that the pilot takes off with what seems like ample fuel, gets halfway there, discovers weather that is worse than expected, has to fly lower than planned, burns a lot more fuel as a result, discovers that they will have to refuel, can't find an airport with good weather at which to land, and ends up flying a graveyard spiral into a fatal crash caused by disorientation in conditions for which they are not trained.
The majority of accidents are traceable to poor planning or decision-making once airborne; and I tend to agree with the other poster that improved avionics are not going to make a really big difference.
1) Continually recalculate fuel remaining upon landing at destination based on ground speed and burn rate. Warn if getting anywhere near reserves.
2) Show nearest filtered airports (those with runways that satisfy both airplane and pilot requirements (max x-wind). If IFR, further filter by approach preferences and if available current wx data against approach minimums.
I agree with you that what you describe is a common accident scenario but imagine a PPL could just hit a single button if they inadvertently enter IMC and the avionics provides a route and vnav profile to make it safely to an airport with low minimums? The most difficult part of flying IFR is that it takes a ridiculous number of button presses on most systems to accomplish that all while trying to also keep the plane straight and level.
In every airplane I've been in that is equipped with both of those, the pilot has access to both projected fuel remaining at destination (in minutes and in gallons), has an ability to get a warning if configurable thresholds are violated, and with just the moving map GPS to have a filtered (usually by minimum length, paved vs soft, and sometimes lit vs unlit) and to have the nearest ("NRST") button present a list of airports, distance, and direction with a single button push.
There are things that could be done to make it better, but I wonder if you're imagining a lower/lesser level of equipment in typical GA traveling aircraft than is currently the case. (To the extent that equipment is already installed that provides 90-95% of the proposed functionality, providing that last 5-10% probably isn't going to be the missing piece of the puzzle.)
Low fuel warnings wouldn't really help in an airplane - from what I can tell most who run out of fuel know they are low for a while but are unable to get someplace to fill up.
Flying a plane is often sort of like that - planning mistakes tend to become problems with large time windows where a warning light is way too late to affect the outcome. Flying into a long narrow canyon is another example where your fate can be sealed minutes before you actually fly into the mountain.
All of this can and should be made better with technology, but a lot of flying hazards are more complex than “warn the user about something happening in the next few seconds”.
I used to have a super old handheld aviation GPS that would warn me something like 15 minutes out if my flight path was going to intersect either with terrain or B/C/D airspace. I guess foreflight somewhat recently added the feature but it still defaults to something like 3 min.
Road navigation is relatively simple and even then there are unexpected road closures and stuff like that. If running out of gas was an emergency in a car you’d never rely on this warning alone, you’d do more careful planning and fuel monitoring. And then cars don’t have to deal with unexpected headwinds, weather (maybe occasionally), closed runways, the list goes on. It’s just a much harder forecasting problem.
Improved avionics could warn you that you're flying into a storm or that the airplane is not airworthy or that you are converging with other traffic.
Complacency kills because it sneaks up on pilots, but it doesn't have to be that way. We should not accept that the FAA's answer is an IMSAFE checklist. Pilots should not have to die simply because they didn't realize they were feeling slightly stressed or emotional prior to takeoff and forgot to check a single one of the 40+ items on the preflight/runup/takeoff checklists.
Of course good pilots should check it all anyway but just as NHTSA requires safety warnings for cars, we could save many more lives if we required low fuel warnings, terrain warnings, gear warnings, speed warnings, etc. in aircraft avionics.