I think there is some slight risk of a reason to change voter sentiment between the early vote and election day but I think it's exceedingly rare. At least for major elections where people are likely to early vote, there haven't been any examples of a candidate having a major stroke or being outed as a child predator between mid-October and the first Tuesday of November (or similar). And for lesser revelations, they're probably not likely to result in the voter's change of heart. Any given voter who is still in-play in mid to late October and concerned about a change in events is well-encouraged to wait.
But the idea that "everyone gets to vote on the same day" makes it sound easier than it is. The push for modern broad-adoption of early voting started in 2004 when some voting lines were 12 hours long (in Ohio for example). People literally showed up to vote but didn't vote because they simply didn't have six or eight or twelve hours to vote. The adult population in the US has grown substantially over the past few decades and expecting everyone to vote on the same day just seems to be inviting major challenge . . . that very easily results in people choosing not to vote, which is just about the worst result we can have (people making the effort show up and vote but then not voting due to capacity or system failures).
If you have limited resources in solving this problem, early voting is far more sensible. You could either (1) attempt to expand the voting capacity system to handle all of the voters in a reasonable amount of time on a single election day - which requires expanding the places where people vote, the number of machines, the number of poll workers, and expanding internal system capacities, etc. . . . OR (2) you actually accommodate the same number of total voters by expanding the days in which those existing locations, systems, and workers will be used, and in-fact it may serve to reduce overall stress on the systems, including on election day, by spreading it out over those early voting days.
It seems like a pretty obvious choice.