To a certain extent, yes, there was rapid obsolescence. This is why, for example, many computers were leased rather than purchased.
Two of the computers I used at university, the EE KDF9, and the ICL 1906A, had operational lifetimes by my estimation of about 7 to 8 years. They were both obsolete by the time they were replaced.
Looking at ICL as a particular example, the 1900 range was introduced in 1964. Its replacement, the 2900 range, was introduced in 1974, though of course had been in development for several years before that.
So that gives the range a lifetime of approximately a decade. However, models within the range get replaced at a faster rate. This chart for the 1900 series shows that the market lifetime of a given model was from 2 to 5 years. The newer systems were upwardly compatible with older systems, as a consequence of a well-defined architecture.
The idea of a computer's "architecture" was introduced by IBM in the System/360, an idea latched on to by other manufacturers, and at least meant that a customer could replace an existing machine with a newer and presumably better implementation, without having to rewrite applications. We're used to that today, of course, since Intel has been pumping out variations on x86 for several decades.
Some inertia accrued from the mere fact that the physical replacement of a large machine in an air-conditioned room took weeks if not months.