Most headphones on the market sport an adapter to convert to 1/4”. I’m looking for headphones that are just 1/4” and don’t need an adapter.
These days, those are going to be rare because so many sources have 3.5mm sockets. If you insist on having a 1/4" connector instead of an adapter, cut off the existing connector and solder in a 1/4" connector in its place. Neutrik makes nice high-quality 1/4" connectors.
On high-quality headphones, the adapter is not an issue. It screws on securely (e.g. Sennheiser do this) so the 3.5 mm pin can't move around in the barrel.
The connector is not an important factor when choosing headphones. What matters is that the headphones are well-matched physically and aurally to your head and ears. If you don't like the connector, get a repair shop to re-terminate it to your preferred connector.