Inventing the transistor was one thing. Being able manufacture it as a reliable and inexpensive product was a difficult long task.
According to the IBM history, at first transistors were made by hand -- someone jiggled the cat whiskers and watched a scope until the proper effect was created. Obviously very expensive and error prone way to go. Even after automation yields of working transistors were low. IBM research not only was developing new computers to use transistors, but also new technology to manufacture transistors and circuit cards. IBM failed to patent or license the manufacturing technology not realizing how valuable it was and let its subcontractors take it and re-use it. (Kind of like PC-DOS).
The end result was that until the late 1950s, transistors cost more than tubes.
Another issue was the learning curve. Electronic engineers by that point had long experience with vacuum tubes--they knew what they could and could not do and their operating characteristics. After the war, both the television and computing engineers extensively studied and developed circuits using tubes and were hesitent to go off on something new and different.
Not all circuits were convertable to transistors, especially back then. I understand to this day electronic guitar amplifier still use tubes.
The president of IBM went around with the new transistor portable radios and had to give an order that all new computers would be built with transistors instead of tubes. One of IBM's early efforts was a transistorized punched card calculator (IBM 608/609) which was more of a prototype and test bed rather than a commercial product.
One popular IBM product, the 650 computer, was made with tubes and remained in production until 1962. Obviously tubes still played a large part in the electronics world at that time.
It is not surprising that TV equipment still contained many tubes. It would do so for a number of years.
My impression is that these days the life cycle of broadcast equipment is relatively short and TV stations and networks replace their gear every few years. However, I suspect back in the 1960s the gear was relatively much more expensive and had a longer life cycle.
I don't know how anyone on TV could stand the lights. I know it was dangerous to look directly into them, but even ignoring them they were awfully powerful and hard on the eyes.