I don't like the way convertibles look. They look stupid. They turn cars that have authority into what appears to be one of those kids cars with no roof. They lack height, authority, and they look all around silly.
https://i.imgur.com/bIRJDXo.png
https://i.imgur.com/3zoCz9v.png
https://i.imgur.com/FM35NDX.png
https://i.imgur.com/kJnxK9G.png
This looks much better to me:
https://i.imgur.com/HkjjPYM.jpg
https://i.imgur.com/tapgFtU.jpg
https://i.imgur.com/LTBiJGI.jpg
There's something respectable and authoritative about metal over some cloth (or outright air when it's down). I would never want a convertible. In fact, I hate them!
I see what you mean, but they're such a status icon that they will probably remain popular. Even if they don't look as awesome, people will buy them just to signal to others that they have money.