I don't think so about the gear.

I tend to see lift but little rotation and no engine pops or spool downs

Lots of possibilities to be explored

Passengers and their phones can be a nuisance but in this case it gives a lot of detail. It certainly enters a heavy shower and is still on the runway when it passes over the upwind touchdown markers. It will be interesting to see if the windshear alert warning was activated during the takeoff run.

This is the reason why in many countries there is no more spin training or single-engine-out exercises during check rides on twin engine GA aircraft.
The number of accidents during such training intended to prevent future accidents made it questionable.

However, if we accept that it is too risky to test it, how can we rely on it to be a safe procedure in case of an emergency? Giving the message to all crews that an evacuation is too risky to test, how do we expect them to take the decission in a real emergency? Just compare with the discussion for the BA in Las Vegas.
Being able to safely evacuate an aircraft is one of the basics in aircraft design and certification. So we should make sure it really works.
It is quite encouraging to see, that in the last 20 years it did. It is the big question whether the situation has become worse since (more carry on, more uneducated passengers...).

All recent accidents showed that:
- there are high risks, passengers do not follow the instructions, crews do not always take the best decissions
- it works

Or engine failure/flameout due to heavy rain... Engines are tested to accept heavy rain in flight, we do not assume that pilots would take off in such situations, we do not design engines to accept any ammount of rain at take-off power, potentially also ingesting additional water from the nose wheel spray.

Some media are already calling the captain a hero. :}
https://www.forbes.com.mx/carlos-gal...-100-personas/ (Translation)
I don't like it when people jump to conclusions, blaming the crew, but calling him a hero so soon...?
Didn't he have enough clues that starting the take off roll was not a good idea? The investigation will tell if he's a reckless fool or a hero or a victim of circumstances...

Can you elaborate on this point? My type doesn't have any limitation for rain, nor advise me to delay takeoff with precipitation.

Pilots are not supposed to perform a take-off in a hailstorm.

Appendix (CS/FAR specific) gives a diagram which requires 20 g/m³ Water up to an altitude for 20.000ft, which is the value relevant for take-off.

Pilots are not supposed to perform a take-off in extreme rain exceeding 20 g/m³ (which is extreme, but happens). In most countries you only encounter such rain in heavy thunderstorms, pilots are not supposed to take off in that situation, especially as you typically just have to wait a few minutes before it has passed.

Aircraft are certified to flown reasonably by the pilot. Every pilot is trained to avoid severe weather.
Sometimes the job of a pilot is to just say no.

THere is ANOTHER video taken from a port window in which is clearly seen that the "storm" is INCREASING during the TO procedure.
When it begins, seems to be a "regular" rainy TO (nothing unusual in lots of places on Planet Earth) but increases once rotation begins.
Possibly metars weren't given correctly to the PIC for the TO calcs...
Just a guess.

Rather than redefining the parameters for an evacuation test, how about using real-life data from the last 10 years? There's been quite a few evacuations, following different kind of incidents and in wildly different settings. 'Real life' data will always give us a better picture of how passengers and crew will act than any simulation, regardless of how well thought out it may be, so why not use that data to see if there are any reasons for change? It should start with a couple of very simple questions: Was evacuation achieved within 90 seconds? If not, what caused the slow down?

we had a mileage restriction relative to thunderstorms which certainly precluded TO in one.

Video
 

Difficult to see on the video but I have the impression that no flaps were set.

The higher the power to more easier it is to ingest rain.

With today's engines the majority of the rain is centrifuged by the fan or diverged behind the fan to not pass through the engine innards. More fan RPM at slow speeds shields the compressor more. In flight low fan rpm and high air speed drives the rain droplets straight.

The cycle of the engines is also important as it affects air to water ratio and the energy needed to process the rain to a gas. Thus the higher the power is good.

Many other considerations enter into this in flight conditions

Looks like a very violent and brief squall with hail and windshear. The predictive windshear would have been inhibited just prior to the time they encountered it . Many warnings are inhibited during T/O until established in climb.
Note that the after crash videos don't show any rain.