Stop saying it's not possible just because Tesla hasn't done it yet.
It is possible to install two compressors to allow pack cooling and cabin heating, or a plumbing/valve system that does both with one compressor. But to what end?
Assume:
Heater output of 10kBTU constant
250 W/mile drive only @ 65 MPH
10kBtu/ 3412 BTU/kw = 2.93kW for heat
65 MPH *250W/mi = 16.25 kW for motion
19.18 kW total
85% of power used for motion
Optimal heat pump case,
COP of 3
No aux heat
2.93kW/3 = 0.98 kW
17.2 kW total
94% used for motion
10% efficiency gain
So in the optimum situation for the heat pump, you get 10% higher efficiency.
This is useful if:
1. You need to make it 10% further to get to a charger/ destination
2. You like saving money/ being the most efficient
How much money?
Difference in heater power usage 2.93 kW-0.98 kW = 1.95 kW per hour
1.95 *2 hours a day *5 days a week * 4 weeks a month * 4 months a year * 5 years * $0.12 per kwH = $188
So if you live in cold (but not too cold) climate, and commute a long way (33k/yr) you save $188 over 5 years.
I'm guessing the extra plumbing, software and such costs more than $188. Even if it is free, if any of that extra plumbing requires an out of warranty (or even in, based on value of time), there is a net loss on the system.
So I would say, yes, a heat pump is more efficient, a heat pump is possible, but a heat pump is not worth it unless you need to squeeze the most range out of your battery pack.