Remote start is huge where I live. When it's -10C and there's a foot of snow you have to dig out in the morning, you can start your car from the app and then start shovelling. The alternative is a hokey pokey of shovelling yourself a path to the car, getting in, starting it, getting out, resuming shovelling. Not the end of the world but it's very nice. Even if there's no snow it's nice to get the cabin above freezing while you're eating breakfast without putting your boots on.
i'm in legit cold canada and being able to open my garage remotely and start my car means it's a lot easier to herd small kids into a warm, comfy carseat.
as for "I often forget to lock the doors"... why do you often forget to lock the doors?
Having just switched from an "old-school" car to one of these "keyless" types, I think the problem is actually self-reinforcing -- the keyless entry and start stuff means you interact with the key less and less so you're more likely to forget to interact with it to lock the car. I can't think of a time I forgot to lock my old school car and yet it's happened more than once with the newer car since I got it a few months ago.
Luckily the other car will at least notify me if I leave it unlocked and can lock it through my phone. Would be nice if it just also auto-locked.
Only if you're like right next to the car. I prefer to remote start my car when I'm more than a few minute walk away from it so it actually has a chance to warm up or cool down. Starting it ten seconds before I get to the car is practically worthless.