For mobile size I usually add burger menu icon on top of the page (or menu links if just couple) with option to open and display all menu links in overlay, but more and more I see approach where the navbar is added to bottom as fixed, where thumb reaches it better. What type of menu would be better to use? People are used to menus on top, but I think this is starting to change.
I think you answered your own question. The discussion is more of: should I follow trends or usability practices?
I argue usability is more important then trends. Like you mentioned, bottom menus are more reachable to the thumb, therefore it is more usable and beneficial for the user.
Trends might dictate using hamburger menus on the top right corner for both desktop and mobile. Maybe it looks good, but it is the worst placement in terms of usability. On desktop, it violates the F browsing pattern and hides all the navigation. On mobile, it is hard to reach. So your choice depends on what you subscribe to: Aesthetics or Usability.
In my opinion, the fixed navbar at the bottom seems far more convenient to use and like you said ensures easy thumb movement, eg: Instagram does a great job in that. But having said that, the burger menu at the top has its own advantages and truly it depends on the user base and the App itself. As a designer you should create both alternatives in design and carry out a/b testing with a few potential users for a better understanding.