OP, you sound totally reasonable to me. You don't mind it being childfree - don't even especially want to go, so don't mind that you can't, and you say at the start you recognise your situation isn't their problem or doing. You just find the increasing wave of twee insincerity around wedding invitations annoying. I'm with you. They are.
I think it's because the editorial staff on wedding magazines are constantly having to create new copy (for what is, let's face it, a pretty generic event) to pad out their thinly-veiled advertorials, and invitation wording is a fertile option. They can present all of these manufactured etiquette minefields, and equally manufactured solutions, and then over time those hastily thrown together articles are accepted as just what people do to be polite for a wedding, alongside spending crazy amounts of money. So you get those awful poems, or attempts to present something clearly in the interests of the couple (nothing wrong with that; it's their wedding) as being in fact their thinking of you. It's manipulative, and most intelligent people find that irritating. And it's silly, because if people just sat down and thought about what they wanted to say, and how to say it with courteous, tactful honesty, and wrote that, it would be far less eye-roll inducing. Speaking as someone who's had both kinds of invitation, they're really easy to tell apart.
Real manners is generally thoughtfully phrased but honest; if you're going to be asking for money/telling people their kids can't come/planning a wedding a long-haul flight away, then be sincere, and appreciative that you're asking for a favour and not doing one. One of the most genuinely courteous couples I know had a childfree wedding, and were upfront about that, but asked that anyone for whom this created a real issue let them know, and they'd work around it (which they did, in the one case where childcare fell through last minute).
I don't blame this couple, and I doubt you do either. They're trying to say something they find awkward as politely as they can, which is never a fun position to be in, and this has been suggested as a good way. But I'm with you, in thinking they're mistaken in that belief.