I can tell you what I don't like about push button start. On my cars I have these ignition key "fobs" that behave like ignition keys, and they have three positions, similar to ignition keys: off, electronics on, engine on.
With the button, you get "off" or "engine on". Every time I get a replacement car that has a button I don't know how to get into the situation where I can sit in the car with the engine off but keep the music playing for as long as I want, e.g. when I'm waiting for someone.
If you have an ignition key or this equivalent system, it's easy.
Now back to the topic. I'd say this screen cutout would annoy me, especially when browsing the web. On the home screen I use a wallpaper that fades to black on top, so it hides it (example attached).
When watching videos just avoid zoom-to-fill and give up some screen real estate. But for browsing and email, which are my main uses, the cutout will be there. I think the notch was better.