Not sure if this has been answered already as I'm catching up on 100+ posts since picking up my MY in Feb to see if there is any new info.
I did (and many others). It's not a big deal - no PoA needed !
Email the delivery team with both driving licences giving your permission and all is good for the other person to collect on your behalf. I took a copy of their email confirmation reply with me but didn't need it, I guess it was already in their system.
Also, the other person asking about Tesla providing private plates; Tesla definitely said no, when I asked this. You have to wait for the V5C to be received by post (a day or so after delivery), then you can assigng the new private plate onto the car via DVLA online which is pretty fast, instant, if I remember correctly,
First get the new plates made up (they will likely ask for your plate retention form), then assign it online, then put new plates on the car and tell your insurance company. (Admiral, you can do that online for £5). If you search back in the thread, you'll see a bit of chat about this (Somewhere from Feb 15th onwards).
Cheers. (...17 pages to go until full catch up)