I think everyone here should be a little more careful with their thoughts.
To begin with, the concept of time has been around long before the invention of clocks and the concept itself never required the existence of accurate clocks. The most fundamental characteristic of time is that it divides our universe (the reality within which all experiments conceivable are performed) into two distinctly different realms: the past and the future! It is an experimental fact supported by observations extending back to before written history that nothing can be done to change the past and that we do not know exactly what the future will turn out to be. The power and dependability of this single idea (that the past and the future are fundamentally different realms) is the central reason for the very existence of the concept of time. To forget this fact is to overlook a very important phenomena fundamental to our very existence.
In the beginning, the concept of time was really a subtle reference to what was known. To refer to a specific moment in the past (usually by naming a significant event, someone's birth, a sunrise or perhaps a war) was to provide a reference to the division between past and future from the perspective of experiencing that event. Time was essentially delineated by a succession of such events. Even prior to the invention of writing, I am sure it was evident to our ancestors that the motion of the sun (among other repetitive events) provided a convenient commonly understood event as a easy reference event. It is my position that this is the real source of the idea behind clocks, devices which could track and label the present. That is, to provide specific references to the collection of interesting boundaries between associated states of past and the future (personal experience itself).
Until Newton came along, I think the concept of time was in good alignment with the needs of mankind; however, I think Newton's great success was the source of a perspective which was fundamentally erroneous. In essence, Newton showed that the future mechanical motion of many objects could be predicted from the past motion via some very simple mathematical relations, time (as a numerical parameter) became a very important scientific concept. This, in itself, was not at all in violation of the concept of time which I have here presented.
So long as clocks are seen as mechanical devices designed to provide a convenient laboratory collection of reproducible repetitive events, then there is no real conflict with the earlier concept concept of time, the division between past and future from the perspective of the events being examined in the laboratory.
Newton made an error when he presumed that these laboratory clocks provided a valid
universal collection of well understood events: i.e. that everybody's clock could be set to agree and thus provide a universal division between between past and future. The power of Newton's achievements, the ability of his ideas to analytically predict the behavior of many events, insured the development of clocks of ever finer precision. In fact, this precision became so important that the scientific society actually moved to the position that "clocks define time"; totally losing sight of the fact that the central issue of time was the division of the past (that which cannot be changed) from the future (that which science is trying to predict).
The scientific community had become so sure that the future was a direct
calculate-able consequence of the past (the mechanical machine paradigm) that they forgot the underlying purpose of the concept: i.e., to separate reality into those two distinctly different realms, the past and the future. They did not feel that these realms were different in any interesting way and thus did not worry about the universal fact that the past is what we cannot change and the future is what we do not know. Absolutely no scientific interest was dedicated to that issue at all.
When Einstein realized Newton's error, (that everybody's clock could not be set to agree) he also realized that it was that fact which had created the problems displayed by the success of Maxwell's equation. His relativity was a brilliant solution; however, his classical education had so tied to the idea that the universe was mechanical machine where the future was a calculate-able consequence of the past that he continued to regard the past and the future as entirely equivalent ("God does not play dice"). He continued to conceive of
time as a fundamental parameter of that boundary between past and future even when he himself proved that it was not (the twin paradox is actually a simple statement that they won't agree with each other's personal time parameter).
Even today, the simple statement that
"clocks to not measure time" is sufficient to convince anyone in the physics community that one is a complete crackpot (that's yours truly if anyone is interested

). No one will even consider the consequences of that suggestion and they will go to any lengths conceivable to avoid even thinking about the issue. The mechanism they use is misdirection of attention! Only magicians understand how easily people can be misled. Misdirection of attention is the very soul of magic; with it magicians can hide the truth for decades even when we know they are trying to fool us (how much worse is it when we trust them implicitly). In science, attention is focused on new ideas, not on the old concepts which are presumed to be clear and consistent; how else could Newton's error have stood for three hundred years? The current error in perspective will probably stand for another thousand years in spite of the fact that this very simple change resolves the problems between general relativity and quantum mechanics.
Someday, they will invent an atomic clock which displays the correct time by definition (see the current definition of time) which is small enough and cheap enough that most everyone can wear one on their wrist. Maybe then,
when none of those clocks agree, it might dawn on someone with scientific authority that those clocks do not agree on the measure time (the division between past and future). I really wish I could get someone to discuss the issue with me (preferably someone who understands mathematics).
Have fun -- Dick