Is wingtip design mature?
The wingtips are a unique part of the aircraft in that they really have one job; minimize drag. Their design is easy to see, and they are a fairly recent addition to transport aircraft. Developments continue to be made in the study of aerodynamics, with modern computing power and methods allowing much better modeling of flow patterns to evaluate designs, and improvements in materials allowing more complex designs to be built.

The key is that the winglet must be properly designed. As wing designs change, the flow over the wings changes, and new winglet designs are invented.

Since it is heavily dependent on the specific application, it's more relevant to look at the evolution of the designs on different aircraft. The design chosen is dependent on the technology available at the time, both for evaluating the design and building it, the design of the wing, intended use of the aircraft, and the previous experience of the manufacturer.

The 737 is an old design that has evolved over time: Original/Classic: none, NG: winglet, P-8: raked tip, MAX: split scimitar

The A330 is a fairly new design: Current: small winglet, neo: winglet

The 747 has also evolved over time, and the latest version shares technology with the 787: Original: none, -400: small winglet, -8: raked tip

The A320 has also evolved over time: Original: none, Current: tip fence, neo: winglet

The A380 is a new design: tip fence

The A350 is a new design: winglet

The 787 is a new design: raked tip

The 777 is a fairly new design: Basic: none, -200LR and -300ER: raked tips

You will notice a trend from smaller designs to larger ones. On larger aircraft though, the weight of a large winglet and the loads it produces can get too large. New designs like the 777, A380, 787, and 747-8 all use either raked tips or small winglets.

As for other parts of aircraft, engines are changing more than you think. The jet engines on the early jet transports look very different from modern high-bypass turbofans. The GEnx engines on the 787 and 747-8 have chevrons at the back to reduce noise. All you see on the outside is the nacelle that minimizes drag; most of the changes go on inside. Also, if you look closely at the front, fan blades on newer engines have curves in them instead of having straight edges.

Most other parts of the aircraft have more complex jobs, not primarily external. A fuselage should be efficient at carrying things inside but also keep drag low. If you look closely you will notice that new planes like the 787 and A350 have a lot in common with previous fuselages, but they are shaped differently as well. It's harder to see the other drastic changes like the use of composites in place of traditional aluminum, electric systems instead of hydraulic or bleed air, fly by wire, etc.

Control surfaces must provide sufficient control while minimizing drag. The size and shape has also changed over time, though the general design has remained.