Several of these "hurdles" are weird to me, as a Texan.
Perhaps in EU (and in older areas of North America, to be fair) you are looking at heat pumps to replace traditional heat sources for heating water for use in radiators, in floor heating, and such, rather than heating the air that flows through the central AC system.
For those of us with a central AC system, with ducting all over the place, we already have our heating and cooling systems intermixed, with regular AC systems having an evaporator either just before or after whatever the heat source is (i.e. electric resistive, natural gas). So switching to a heat pump involves replacing the AC system, and if you don't replace the furnace/blower unit, you also slave the old furnace to the heat pump for "emergency heat".
Many already have heat pump systems for heat, from when their house was built (or when they last replaced the entire heating/cooling system) in which there is likely still a resistive heat element as "emergency" heat (for faster warm up and/or if the outside temp drops below operating conditions for the heat pump), and the evaporator and condensor basically switch roles as the AC system runs in "reverse" to pump heat from the outside in, rather than outside in. AC systems are, after all, heat pumps - just traditionally one directional. "Heat pumps" are generally bidirectional heat pumps (or at least, one directional, but switchable, depending on how you want to define it).
So complaints about noise (we already have noisy outside compressors for cooling), space (it takes up the same space, more or less), piping (might sometimes require a change but usually can get away with the same piping, and even then most such houses aren't that hard to change out the refridgerant piping for), vibrations (our outside compressors/condensor/fan units are usually installed on concrete pads, sometimes with extra padding between the pad and the unit, which is typically separate from the house slab or other foundation support), and power draw (we already have high power connections for the AC, we're just running in reverse, so it's the same power more or less), sound weird from my perspective.
However, if you're in an area that never uses central AC, with at most quieter mini-splits or possibly nothing, and primarily needs heating, then that's certainly some potential for disruption I suppose, if you can solve the pain points for buildings that never had central AC. I'm not sure that Tesla has anything other than a willingness to engineer new solutions as an advantage, though, since they're not really inventing anything new, just packaging it smarter, with regards to heat pumps.
Other than as yet another premium expensive thing they can sell to higher end homeowners (i.e. like power wall and solar roof), I don't see much of a market for a Tesla branded central air system in competition with traditional central AC.
Perhaps they might be able to come up with a new way of doing things as a replacement for non-central air systems that use heated water or such to transport heat, but the way everything would scale up, to support a house sized load, and the lack of alternative heat sources to scavenge (even if you could scavenge heat from the stove or whatever, that's not useful to the stove's operation, and if the purpose is heating, then it's already helping heat it's immediate vicinity).
I suspect for that scenario, at best, they might provide a premium outdoor unit that is quieter than the competition, and possibly a bit smaller or at least packaged differently (i.e. a tall rectangle rather than a large cube), to address the concerns you listed as being problems for getting one in your locality. Assuming they intended to re-use their existing designs, by going from AC to HVDC to drive ~400V heat pumps (but upscaled), you'd be adding extra inefficiencies in the conversion from AC to DC, so the HVDC compressor would need to be more efficient than a traditional one run from AC. Perhaps the efficiency might be gained as the average over time, by being able to run at different speeds.
But I do think you've raised an interesting point of discussion - we don't all think of the same thing when we think of heat pumps and heating (or cooling) a building. Some of us expect central air, and a heat pump is just a fancy AC unit that can run backwards, and other than the cost to install the unit there's no material difference between them. Others, such as yourself, clearly have a different expectation, whether due to being a different climate, different local regulations, or so on. So there may be different markets better suited to different solutions, and thus a potential Tesla system (or systems, to address different markets), will have different competitive advantages (or lack there of) depending on what they're competing against, and trying to achieve.
When we discuss these things, we probably need to be clear as to what type of system we're envisioning, or half of us are going to think the other half are nuts and vice versa.