No they don't. Just wait for Tiger Lake U reviews.
Magic of "more cores" doesn't work on most consumers. Thankfully.
Much touted? You mean: much discussed by enthusiasts on forums like this one where most people stay on desktops anyway?
Intel's most important client for high-end -H chips is Apple.
If Apple really plans to replace Macbook Pro with an ARM system (which Intel surely knows by now), they'll have even less reason to invest in the -H lineup.
I mean, 20 years from now, they'll probably sell just server processors and -U SoCs. So budgets for developing high-power mobile and desktop chips will probably be decimated over the next decade anyway.
If Intel isn't able to make an 8-core mobile competitor for Zen2 out of Tiger Lake, they may just sacrifice this market altogether.
An even if they can, it might not be an interesting niche.
They've already given up on HEDT - a move that was expected already before 2017 - when the main treat from AMD was that it'll collapse and US gov will force Intel to split.
I agree with your multicore comment. I'm not swayed by more cores in a laptop and patiently waiting for Anandtech review on Tigerlake. Looking at leaks, it looks impressive (great single core and multicore comes close to an 8c by AMD) but I am waiting on power consumption and how hot it gets. If it gets hot quick and sucks power, I'm getting a Renoir laptop, if not then it will be Tigerlake.