I'm gonna share my opinion. If it's a question of getting home, a rope plug should allow you to re-inflate the tire, after removing the nail. Carrying a 'mushroom' plug and the inserting tool isn't something anyone is likely going to do for around the house riding, maybe on a trip away from home. I've used a rope plug to get-home before, but being close-to the side of the sidewall like yours, I bit the bullet and replaced the tire.
I once installed a new Dunlop, it was a week-old and I was doing errands when I left the bank and returned to my bike, to find the new rear tire flat. There was a 'foreign object' in it, more-towards the center than at the sidewall. I slowly returned home, which was only about 1 mile away, and parked the bike. To repair the tire, I removed it, and patched it with an inside-the-tire patch, and put it aside to use for a 'roll-around tire' on a bike being worked-upon, but I never considered using it to return it to service. That's just me, you may be willing to play the odds. I'm not. BTW, the 'foreign object' was a Craftsman allen wrench, a very-small one, and it went-in just-like a nail, and it stayed there while I rode home. It's still in the top shelf of one of my toolboxes to remind me.
Yes, trashing a new tire is a bit of money, but if I wrecked because the patched tire failed, causing a wreck, what's the cost? I know there are plenty of people who will enter anecdotal stories about repairing a tire, and riding with it, but for me, I'll buy a new one, and do the same, next-time it may happen.