Great question! For sake of this answer, I'm going to assume that by reliable you meant accurate, since that what your question seems to imply. Now, compared to our modern atomic clocks or even quartz movements, clocks in the 17th and 18th century were not nearly as accurate. The thing is, that wasn't really an issue for most people (most being the operative word here that I’ll get to in a moment). As far as public timekeepers were concerned, they were mostly and auditory technology, meaning that the public learned what time it was by bells and other sounds rather than looked at the dial. For most people this was perfectly fine, as one’s day to day life was structured through a rough combination of natural time markers like sun rise/set and those bell towers ringing out the hours of the day.

This gets us roughly to the 18th century when personal clocks and watches started to become more affordable to larger numbers of people. It is in this period when we see more and more timekeepers counting minutes and even the odd second hand (my god!), but accuracy was still a socially regulated phenomenon, meaning that people would self-regulate their timepieces to match those of people in their immediate social networks. I’m sure you can see the issue here. Let’s say you’re a contract laborer who has agreed to work for some local proto-industrialist, or whatever, for 8 hours in a rural town that doesn’t have a public timekeeper. In this scenario, the only person that has a clock is the person who hired you. Well, if they’re clock is running slow, then you’re working for much longer than 8 hours, but there is no way to know that. The accuracy of any given timekeeper was only determined by people who had timekeepers. There was no real need for an objective accurate time since the ‘true time’ was constantly being negotiated.

Now I mentioned at the outset that this was true for most people. For astronomers, accurate timekeeping was essential and was what drove much of the horological innovation in this period. Its what got us the minute and second hands, as well as the pendulum clock. Now, in the early to mid 18th century, one of the most pressing issues facing European scholars was calculating longitude at sea, a topic that others have covered. Now the issue of whether or not John Harrison deserved the longitude prize for his H4 marine chronometer isn’t as important as how it was understood by the public. To put it simply, by waging a publicity campaign against the Board of Longitude for decades, Harrison had helped to effectively turn the accuracy of timekeepers into a major selling point. So much so that by 1766 clock and watchmaker/vendor Joshua Lockwood could advertise to his Charlestown, South Carolina neighbors that the watches he sold had components borrowed directly from “Mr. Harrison’s machine.”

So we see that over the course of the 18th century, timekeepers became relatively more affordable and accuracy became more of an issue for consumers. Both these factors were magnified by the consumer revolution which began around the middle of the century and really took off once accuracy began a point of national pride, with British clock and watchmakers trying desperately to deter people from buying cheaper Swiss knockoffs that were less accurate than the real-deal pieces made in England. As more people came to own timekeepers that were more precise (not accurate), the need for a less precise public clock lessened and lessened. Couple this with the move towards more privately regulated timekeeping practices in the industrialization period of the early 19th century, and we effectively reach a point where the accuracy of timekeepers became a crucially important aspect of labor struggles over the working day.

further reading: David Landes, Revolution in Time 2nd Ed. (Harvard UP, 2000); E.P. Thompson, “Time, Work-Discipline, and Industrial Capitalism,” Past & Present (1967); Gerhard Dohrn-van Rossum, History of the Hour (Chicago UP, 1998). For eurocentrism critiques of Landes see: Ogle, Global Transformation of Time (Harvard UP, 2015). On Thompson’s overemphasis on a division between inaccurate natural time and accurate clock time see: Glennie and Thift, “Reworking E.P. Thompson,” Time & Society (1996), Shaping the Day (Oxford UP, 2009); Mark E. Smith, Mastered by the Clock, (UNC Press, 1997); and Mark Hailwood, “Time and Work in Rural England, 1500–1700,” Past & Present (2020). Also of interest: “Viewpoint: Temporality”, Past & Present (May, 2019).