You don’t need a new technique
You don’t normally stall jetliners. And in a crisis the last thing you want to do is learn a new technique.
Besides, they already have a trained practice for descending jetliners very quickly. It’s used for loss of cabin pressure. While the procedure normally levels at 10,000’/3000m, it could certainly be extended.
Anyway, descent time has not been the failure point
When you look at fire-on-airplane tragedies, the pinch point has not been inability to make bare-minimum time to landing/evac. The problem has been pilots overestimating the time they have available.
Look at the UPS Air tragedy and go figure where they were in the airspace at the first sign of fire. The closest large airport with facilities was an Iranian military base on a nearby island. The second closest large field was Doha, Qatar. They decided to return to Dubai.
Now, think about that decision-making. Iranian military base with a US-flagged airliner technically in the US military reserve? Yeah, not an ideal situation. Doha, this was obviously a maintenance problem and they didn’t have a maintenance base there. Dubai was only, what, 10 minutes further.
And of course, as is very typical in these flights, they continued moving away from Dubai after the first sign of trouble, until they chased the problem a bit and concluded yeah, they really did need to return.
So we have a number of potential saves on the table, but they did a careful analysis and made a more preferential choice given a number of factors. The time spent making those choices sealed their fate.
Then we look at the flight that went down off Halifax. Again, the first sign of trouble, and indeed the second sign of definite fire, happened fairly early - and they still had a variety of divert airports (some not very good choices for a fuel-heavy jetliner). They chose Halifax, which could’ve worked if they had realized they were on the clock, but then they piddle-diddled in the air with a great deal of time-wasting communications and procedural stuff, until they were overcome.
Why not just beeline for the nearest airport?
The problem is that, early on, the signs are ambiguous. Those early signs are often seen without an ensuing fire. So the pilots are concerned with being perceived as alarmist or “making the problem up” if it turns out to be nothing special.
And a divert complicates things. The descent, landing, takeoff, climb and resumption of flight takes fuel that wasn’t allocated, which means the turns-out-to-be-nothing aircraft must buy fuel at the divert airport - where they may not have a supply contract.
Either company or a perhaps non-contract FBO (independent mechanic) qualified on that type must be found and/or flown into that airport, to clear the plane for continued flight. (If it’s nothing). Meanwhile the added time will put this aircrew “over time” so they will not be able to finish the flight. New aircrew must come in also.
Likely the most expedient way to get people on their way is for the airline to bring in another heavy, and pay more landing fees at an airport where they do not have a contract, other aircrew called in, etc. This may take enough time that the airline has to book every hotel in the 3 nearest towns, and find transport for them all, which basically involves getting someone from the local middle school on the phone on a Sunday.
Like the Halifax case, it may involve hundreds of people going through immigration in a country they might not have a visa - heck, it creates another crisis if they land a 300-pax jet at an airport with no Immigration facilities (or a small one sized for 12-passenger rubberband planes). Remember they “skidded to a stop” on the runway, deployed slides, and pax fled the aircraft, and are all over the airport, hopping the fence to seek help at neighbor’s homes, even venturing into town. Hey, that family that US CBP was deporting, escorted onto the plane and stayed until we pushed back - has anyone seen them?
So diversion creates a Big Mess, and needless to say, the pilots do put some energy into avoiding it. And that means time... tick tock, says the fire.