Other than 37signals, which large tech companies do this? Large tech companies have smart engineers. If turbolinks really were better, why haven't they caught on?
I sometimes suspect it's because most web development is boring and to make it interesting smart devs make tools and frameworks instead, even when it's not really appropiate.
Is the Facebook interface today significantly better than it was 5 years ago? No. But they've invested a huge amount of time in React in that time, so why isn't it?
I'm going to play devil's advocate here. I totally hear you re: everything being built in React nowadays and SPAs are annoying both as a user and a developer, I definitely feel like that sometimes.
But the answer to your question, why isn't Facebook significantly better than it was 5 years ago, is exactly because they've invested a huge amount of time in React etc. and now utilize them fully to build many more features on top of it.
5 years ago, your notification bubble would often go out of sync. Your inbox chat might be on a separate page (can't remember if they had the bottom chat bar in 2012 yet). Even if it was, it definitely did not have video chat and voice call straight from that. Notifications didn't appear at the lower left in addition to the notif dropdown. I could go on forever.
It is very similar to mobile phones cpu/memory and battery. Battery tech is getting better and better, why do phones in 2017 still only last < 24 hours, instead of 3 days? It's because battery got better, all the phone manufacturers (Apple, etc.) made use of that extra power and put better cpu/memory in their phones. Now if phones have better and better cpu, why are newer phones in 2017 still feel as sluggish as the ones in 2007? Again, it's because the phones have better cpu now, mobile OS and software developers put more and more features in their code and make use of all that extra cpu resources.