Vesting on a startup founder’s shares can perhaps be thought of as "insurance" for people other than the founder, especially co-founders and investors (and even future employees and other key business partners). During a startup's critical first years in its efforts to establish a viable business, vesting of the founders' shares offers these key people a degree of assurance that the founder is incentivized to see the startup through this critical period. Vesting also offers both the founders and these key people a clear, upfront understanding of what will happen in the event a founder stops participating in building and growing the startup.
It is virtually unheard of for a well-informed startup with more than one founder to issue its founders 100% fully vested shares. A web search for "founder stock vesting" illustrates that there is nearly unanimous consensus that a startup with more than one founder should impose vesting on the founders' shares. Below are links to reading materials on this topic from some of the top startup lawyers, VCs and founders on this topic:
As noted by Y Combinator partner and general counsel Carolynn Levy, even a solo founder should typically subject her shares to vesting from the beginning because most solo founders anticipate bringing in future co-founders, investors, employees or other key people (search for "Do solo founders need vesting" in transcript of Legal and Accounting Basics for Startups). By subjecting the shares to vesting from the beginning, the founder’s vesting clock is started and reflects the time she has been working on the company. Among other things, this reduces the risk that she will have to impose vesting at a later time and potentially re-set the vesting clock.
Consult an attorney if you have questions about your specific circumstances.