I created a site collection and subsite in SharePoint 2016. I'm a SharePoint administrator so I have full access. I can create custom lists without issue, particularly with the respect that my lists display the + new item above the list.
PersonB is a poweruser with the ability to create lists. At first, the list seems normal, but after a while he calls me and complains that the list has lost the "+ new item or edit this list" option along with the view selection. I see the same effect on this list.
To get by, I edit the list page's web part and change the toolbar type to "Show Toolbar". This at least presents dropdowns of new, actions, and settings. Oddly enough, there also appears a green + sign and add new item below the list as if it were a SharePoint 2010 experience instead of SharePoint 2016.
This list was not imported from a previous template. The site was created new in SharePoint 2016. Results are the same on IE, Edge, and Chrome. Permissions are adequate and the isn't any problem on any other list in the site.
EDIT: I found my answer. This seems kinda odd..but... The poweruser modified the view style to be a "Basic Table". I set it back to "Default" and we're back to the SP2016 style.
Hope this helps someone else.