Interesting. Perhaps I need to study what physicists mean by 'mass', because right now I'm having a hard time understanding how something without a mass can exist in time and space. I often find that the best way (for me) to understand something difficult in science, is to read what philosophers have to say about it! E.g. just found a book that's only about mass and its history: https://press.princeton.edu/books/paperback/9780691144320/concepts-of-mass-in-contemporary-physics-and-philosophy
So maybe I'll read that in the future. But I worry that by the time I do, scientists will have changed their models!
I don't know how to explain this better. Sorry.
The way those massless particles behave is entirely dictated by special relativity, so that this is by far non trivial (and not high-school level). Those particles for instance travel at the speed of light. Moreover, they feel gravitational fields (that's general relativity), even with being massless, etc.
The story is far from trivial, as can be guessed. The point that can maybe make it clearer (who knows?) is to recall that we discuss at the level of the microscopic world and not the macroscopic one. Things are very different in there.