That is why Crysis 1 has more advanced tech compared to Crysis 3. People didn't even notice this because Crysis 3 has the more advanced art.
This simply isn't true. Crysis 2 was a graphical leap over Crysis 1. Crysis 3 was a graphical leap over 1/2 that pushed things further. It's a simply stunning look game. And in turn, Homefront: The Revolution built upon the foundation of Crysis 2 and Crysis 3 to push things even further. Yes, it was developed by Crytek UK but it was a Crytek game. If Crytek hadn't run out of money they would have eventually published it.
Crytek is dead. All the capable Crytek guys are working at id Software Frankfurt (Bethesda).
While Crytek endured a lot of talent bleed and may never return to former glory, Hunt: Showdown is ample demonstration that the company has still "got it". It remains to be seen how well Star Citizen turns out, but it's interesting to note CIG are essentially attempting to execute the procedural generation techniques Crytek toyed with during the development of Crysis 2. If Squadron 42 doesn't suck, or even if it does suck but executes either technical or mechanical ideas really, really well -- the industry will sit up and notice and ask, "Can we do that?" After No Man's Sky came out, Bioware wanted to follow in its footsteps -- they wanted Andromeda to be a game set in a vast universe you could freely explore in your ship. But unfortunately they ran into issues with the planet generation system and such. I imagine there's a lot of people who don't think No Man's Sky is technically impressive. But it is. It really is. Particularly nowdays.
Also, on the topic of Crytek, they did great work in VR with Robinson: The Journey. Their voxel-based global illumination system is really quite good. Crytek were always ahead of the curve and perhaps they're a demonstration of how business reality butts up against technical ambition.
You are mixing up efficiency and effectiveness. Cry3 was more efficient (because they switched to industry-proved tech) and that is what the trailer is about.
They pioneered much of that "industry proven tech". Crysis 3 built upon the foundation of Crysis 2, and its tech. There are some good presentations on their work in Crysis 2.
http://www.klayge.org/material/4_1/SSR/S2011_SecretsCryENGINE3Tech_0.pdf Crytek had some of the best engineers working in the industry. And some of the best game designers. They still have some of the best game designers and engineers -- just look at Hunt: Showdown.
And as I mentioned earlier, Homefront: The Revolution built upon Crysis 3. It introduced a very interesting prebaked large scale ambient occlusion system that works with dynamic weather and ToD systems. It's the underlying reason why the game's HDR implementation on consoles is so applauded.
http://www.dsdambuster.com/blog/lsao-part-1
People in the industry constantly look at what their peers are doing. Designers want their games to be as good as possible whether that's audio, visuals, UI design, controls, general mechanics. That's why the industry has presentations at GDC where they tell their peers how they accomplished the things they did. Naughty Dog's engineers are respected because they're great engineers. Infinity Ward's engineers are also respected because they're great engineers. Did you know Call of Duty: Infinite Warfare has 40ms of input latency? Doom 2016 has 80ms, and that game is a technical triumph that builds upon the foundations of Crytek's work. You know why? Because Tiago Sousa departed Crytek and joined id Software in 2015. He and other engineers have done amazing work that has featured in DOOM 2016, Wolfenstein II, The Evil Within 2, and the upcoming DOOM: Eternal. Modern id Tech takes a number of core rendering concepts from CryEngine. He also co-created SMAA anti-aliasing, I believe.