Would longer runways allow pilots to cancel a takeoff for failures that right now are too far into the takeoff to allow for a deceleration?

Yes, but not in a particularly useful way.

Having more runway ahead will always make pilots happier and provide more options for emergency which will translate to improved safety (hence Edwards AFB using the lake bed), but in terms of the question, the time window between V1 and rotation is very narrow, with very few classes of problems likely to occur there (ie already rolling at takeoff power and traveling in a straight line). Single engine failure during roll is certainly possible but that is why current standards require ability to complete climb out with one engine failure.

More common are problems/failures between starting rotation and getting into clean climb out configuration, many of which either cannot be detected (errors in balance or load) or only occur (issues with controls, flaps or undercarriage) during rotation and climb.

Longer runway would certainly help the cases where aircraft starts rotation/leaves runway but decides not to fly today, but since you are now talking safely allowing a full landing of an aircraft over their design touchdown weight you need a LONGER than normal runway sited outside the existing airport boundary, one for each current runway, not just making them slight longer.

Where the issue is aircraft needing another couple of hundred meters more runway than fits inside the available space there is already a known solution in form of Engineered Material Arrestor surfaces, which do damage the aircraft when used but generally anything that means aborting post V1 is probably already pretty catastrophic, at help keep whatever bad thing happening contained to the airfield and in reach of the emergency services there.

If this question is looking at actually actionable safety improvements in this area, wider and more standardised deployment of EMA would be a valid cause.

As was noted in the comments, if politics and city planning(say if humans lived underground) allowed much longer runways than we currently have, what we would probably see would be a combination of aircraft with higher takeoff/landing speeds due wings being tuned for more efficient cruise flight and running engines at reduced takeoff thrust for longer life using the available distance.

Yes, in a way, but pilots can cancel above V1 already.
The effect on safety is about linear for runway length, i.e. twice the length, ~half the accidents. Pilots try to pick long runways if a diversion is needed due to malfunction or weather, although weather is still key.

Constrained short fields like Courchevel and Yrasquin are infamous for high fatalities, while large international airports are the safest. Width and quantity help too: multiple runways allow avoiding crosswinds, wider runways make crosswind landings easier.

Speaking specifically of aborted takeoffs, it doesn't take a very long runway to abort. The stopping distance for a 737 at 80 kts is just about 300 meters. The current requirements are generally sufficient, but with little headroom. Also, while aborting above V1 can damage the aircraft, most overruns end without loss of life if the runway safety area is extensive and clear of obstructions.

But you can't just make every runway longer, because that land is often taken up by something else. When there's space available, airports tend to have longer runways than mandatory.

From a regulatory standpoint, it's a quantity vs quality tradeoff. If airports have to be larger, they'll be fewer in numbers and further away from cities. This means more traffic per airport and longer drives to the airport. Statistically, 1 mile driven is approximately equal to 750 miles flown in terms of risk.

The best safety improvement is to improve areas around the runway. Installing EMAS on both ends of each runway. Ensure that runway lights and ILS antennae, both of which are usually hit in runway overruns, are frangible. Extend runway safety areas. Zone approach areas to forbid tall or dangerous buildings like gas stations for as long as practical.

All of this has been done, is being done and has successfully prevented or greatly reduced the loss of life. A modern 1000-ft RESA with EMAS is almost as safe as a longer runway. New airliners are built with more crash protections than the best of cars, so it makes more sense to make the few accidents that occur safer than to close airports that can't be expanded.

Yes, they would. If you had a 100km runway, for example, you could land straight ahead in the event of an engine failure in the first thousand feet in pretty much any type.