Both programs have been dead for years, FluxBB has merged with another software and PunBB has been abandoned by its owners.
phpBB looks horrible, I agree, but versions 3.1 and later have at least appropriate plugins, etc., as well as pretty responsive free themes. The free themes of myBB seem almost all broken, like SMF which also stagnated like Pun / Flux.
Not a big fan of XenForo or modern IPS, but IPB3 and vB3 are extraordinary. It reminds me of the old days, the mobile layout of vB4 is a wreck and the less we say about anything about v5, the better it is. I tried an unencrypted IPS4 for testing purposes and, while it was whimsical, it was a lot more cluttered than the IPB3 was on the same server.
Honestly, I would use MyBB if the light-sensitive themes were neither garbage nor breaks … I do not know how to style a website artistically, even though my HTML / CSS syntax is in fact quite good.
And the IMO, the things that try to differ from other forums and offer something that tries to attract newbies better will not work well. This alienates the user base and doing nothing because the users they are aiming to attract will not go to the forums anyway, they will turn to Discord or a proprietary IM group.