There are better ways to keep yourself safe than invisibility,
Not many, especially for someone too young to have the raw magic for most powerful spells. When it comes to protection, having no one know you’re there is the next best thing to not being there.
Additionally, Harry’s first instinct when he realised how much personal danger he was in was to wear the Cloak 24⁄7. It seems odd that this instinct is 100% absent now that his survival also represents the survival of the entire world.
I don’t think that’s realistic. Harry’s acknowledged that he needs to mature into a worthwhile adult in order to be able to save the world, and he’s not going to gain the experiences he needs to do that (or indeed maintain a reasonable standard of mental health) by becoming a full-on hikikomori.