Nope.
Nope.
Certainly there are grammatical differences between Hochdeutsch, Plattdeutsch, Allemanisch, (much less the varieties spoken in Switzerland!) in addition to accent and (minor) vocabulary differences so I presume you aren't disagreeing with that. I have been to plays in Munich that were explicitly in Bayerisch and were deliberately incomprehensible (have had the same "problem" in Edinburgh). So I doubt you disagree with that.
Do you disagree that people use Hochdeutsch at home? All I can say is that my kid grew up speaking Hochdeutsch at home because his mother (from south of Hannover, near Goslar) speaks it in the house, as do the rest of her family, neighbors, etc so it's what he learnt when learning to speak. In Berlin and in the overseas German School the kids all commented that he was the one who didn't have to learn the accent (in the overseas school it was very clear that all the kids had different accents).
I assume he disagrees with your claim that almost nobody speaks Hochdeutsch at home (which you even seem to contradict yourself).
I only know German as a second language (so have only studied Hochdeutsch) but I have the impression that it's rather common as a home language today. One reason may be that there are more couples than ever before who've come from different regions of the German-speaking world, and hence have Hochdeutsch as their main common language.
* people who speak Hochdeutsch generally also speak Hochdeutsch in private
* people who speak Swabian or Bavarian generally speak it both at home and in public
* most other regional dialects have moved closer to Hochdeutsch, usually retaining only a few "loanwords" and the accent
A great example of the last one is the Cologne dialect: because of its association with Karneval it is frequently emulated in TV to the point that what most people think of as dialect is just a Rhineland accent with a handful of dialect words thrown in for flavour. The result is comprehensible for speakers of Hochdeutsch but about as authentic as mock "ebonics" sound to an actual speaker of AAVE.
The Cologne dialect of course still exists and there are some people who still speak it but retain a heavy accent when switching to Hochdeutsch. But it's become exceedingly rare even among natives.
Similarly what passes for Hochdeutsch in Swabia is often still heavily accented and full of Swabian phrases to the point that the state of Baden-Württemberg ran a campaign with the slogan "We can do everything but speak Hochdeutsch". "Foreigners" are often confused by the Swabian phrases that are mixed into what Swabian speakers would otherwise consider their best attempt at Hochdeutsch.
Compare this to Saxony "Hochdeutsch" which is often very difficult to understand due to the thick accent but tends to contain far fewer dialect vocabulary.
In other words: when talking to Swabians in "Hochdeutsch" you might generally understand the gist of what they're saying but will have to ask for clarifications on certain words they're using; when talking to Saxons you'll probably just have to ask them to speak more slowly and enunciate words more clearly ("What does a Saxon say when he wants to buy a Christmas tree in New York? 'Attention Please!'").
These are all generalisations but I'm a Cologne native who spends a lot of time in Westphalia and have been to various parts of Germany, so I think my observations might be somewhat representative.
The general historic trend seems to be that dialects have shifted towards Hochdeutsch vocabulary (with a few notable exceptions like Swabian and Bavarian) and in most places even the remaining accent has faded almost entirely.
After 2 years and doing an internship in a workplace where most of the people were Swabian, I could understand it quite well and could even speak a little. It was quite amazing how continual exposure to the dialect made it go from nonsense to normal.
I was amused when I spoke with Germans who seemed apparently unable to speak standard German despite hearing it everyday from TV, radio, and non-Swabian speakers: they could only seem to speak in their Swabian dialect. What was even more amusing is when they spoke English and their Swabian accent came through into English as well.
However his English has improved quite a bit over the years, although some would argue this has made him more unpleasant.
"Tännchen" is the diminutive of "Tanne", meaning "fir".
So a Saxon who doesn't know what a fir is called in English might ask for "A Tännchen please" -- which would sound almost exactly like "Attention please".