I am constantly finding products that interest me, and have no hesitation of putting my unaliased gmail address into random product sites.
You may be surprised to learn that my inbox is not a cesspool, there is nothing in there which I didn't ask for.
I believe the aversion to spreading email addresses online is actually a holdover emotion from a time when spam was an unaddressed real problem and where obfuscation was possible.
Today, your and my email address are already in hundreds of purchasable lists... and the battle is fought by gmail instead of by me.
Agreed, spam prevention has come a long way on both the client-side (gmail) and regulations (CAN-SPAM), forcing clear unsubscribe paths. Yes, the damage of past behaviour is hard to reverse.
Next generation of users don't allot much attention to email, so liking/following is the way to "subscribe to product info". Otherwise, those exclusively email-based popovers are just a nuisance to that audience; good ones include other channels.
My guess is that they see it as "oh I like this a lot, I'll sign up for more so I don't have to remember to come back and check this site."
ctrl+tab actually feels a bit awkward on my MBP and only shows 5 tabs on FF Nightly; seems to be sourced from the most recently used ¯\_(ツ)_/¯
The experience _can_ be ok, if it's easy enough to dismiss. The pattern that drives me a little nuts is the "intent to close tab" event trigger. I just wanted to switch tabs, calm down, I'm not leaving your site.