No, that's just how Linux is. You have a bunch of libraries floating around that are shared by programs and you need to make sure they're there. Usually there aren't that many, but Houdini has a broad range of abilities and uses a lot of them. There are different workarounds for it like Flatpak or even Nix that behave as you described, but you're not going to be able to use those now.
The list is available
here [
www.sidefx.com]
But as you can see, Arch-based distros aren't officially supported. That only means you need to figure things out yourself, don't worry. Houdini will work on CachyOS.
Here are our Arch equivalents that I used and they seem to work:
sudo pacman -S alsa-lib cups dbus expat fontconfig glib2 glibc curl libdrm gcc-libs libglvnd libice libsm util-linux libx11 libxcb libxcomposite libxdamage libxext libxfixes libxi libxkbcommon libxkbcommon-x11 libxkbfile libxrandr libxrender libxshmfence libxt libxfst glu ncurses nspr nss xorg-server-xvfb pciutils xcb-util-cursor xcb-util-image xcb-util-keysyms xcb-util-renderutil xcb-util-wm
If you install these, I believe Houdini should boot up and let you click things. Lastly, installing X11 is simple and you can switch between Wayland and X11 on the login screen at any moment. Installing X11 usually requires just a couple of packages, something like this for Plasma:
sudo pacman -S plasma-workspace xorg-server
(Warning: I've never actually used Plasma, I don't know if the above will work for you. I use i3wm and all I need to install is "i3 xorg-server" to make it happen)