As someone who has always been a flip-phone user and a major advocate of davka using flip phones and being anti-smart phones, it pains me to say this: it’s just purely an arbitrary social norm at this point.
If true flip phones were still commercially available then this wouldn’t be the case. There would be real arguments for flip phones, which are still the arguments people are making despite being outdated. The only currently available flip phones are smart phones. Yes, you can have stuff done to them by frum organizations to dumb them down, but you can also do that with touch-screen phones.
The Cat phone is a great example because not only is it a smart phone, but it’s a straight up touchscreen! It just has a numpad hanging off of it for no reason.
Unfortunately, I would guess that the future will not see a revolution of true flip phones coming back. More likely, people will either conclude that it’s pointless to have a flip phone if it’s a smart phone anyway and just get regular smart phones, or people will double down harder on the flip-phone-cultural-status thing you’ve observed. I genuinely have no idea what I’ll do when my current flip phone kicks the bucket. I hate pointless social norms, but I really really hate touchscreens…