Just like your "opponents" are over-generalising, you're deliberately picking the most extreme examples to make your argument. (Batocera as a daily driver - you know that's what Hanna Montana Linux is for!)
My Linux axioms are: for most new users...
- choice of DE is most noticeable and decides whether they like their initial experience.
- choice of base distro family does matter a lot in the long run (Debian-based vs. Arch-based vs. Redhat-based); if you stay inside the same family (e.g. Pop!OS vs. Ubuntu vs. Zorin vs. Mint), choice matters a lot less (and DE is most impactful, c.f. point one).
- choosing a distro with specialised security hardening (immutable systems, Nix, Qubes, Bazzite) does matter; most of these will make new users unhappy or even question their sanity.
Where you are right: yes, the choices embedded within these three axioms do matter a lot and are noticeable, so it is helpful to have an experienced user recommend a distro to you when starting out.
Where the "distro don't matter" people are right: there are a lot less choices to be made than meets the eye. Effectively, it can be boiled down to three.