But why would you use an all-transistor design these days? We don't still use the CK-722 Germanium transistor and not many new designs will use a 741 op amp. Things change...
The analog companies are all still in business making new devices all the time. The engineers wouldn't design a circuit using all transistors because there is no motivation for doing so. But I don't doubt for a minute that they could do it.
Actually, the answer to that question, is quite simple.
I don't know the latest world wide figures, as to how many of the following designs, still need to be created.
But there is a need to design new ICs (ASIC's, full custom ICs and similar such things), for all sorts of application areas.
E.g. A new sensing technology is invented, and it is expected to sell and be produced in the tens of millions each year.
Perhaps a new acceleration/motion detector, for the latest games console controller or virtual reality or car sensors etc etc.
That may need one or more, brand new designed, fully custom (or similar) all analogue ICs to be designed.
No op-amps or digital gates on it at all. Just 20 (or 5 or 50,000), cleverly placed analogue transistor designed, circuits.
So in order to design this new, all analogue (transistor) IC. It needs, clever, experienced analogue design engineers to create it.
Even if it goes to an all analogue design, but uses op-amps, via an IC ASIC design. It still needs analogue designers to create it.
Also, there are plenty of mixed, analogue and digital, custom ICs. Sometimes including MCUs.
The analogue bits, still need analogue designers, even if the onboard MCUs needs other types of engineers (software etc).