Traditionally, at least as late as 1860, it was considered crass for a presidential candidate to personally campaign for the presidency. I.e. they normally didn't go out in public for campaign purposes.
Part of this was that for the first century or so, it could take months to travel from one state to the most distant one. It's only in the last century or so that it was possible to travel from Maine to Georgia in just a few hours.
This is somewhat confused in that we talk about things like the Lincoln-Douglas debates as being important in the 1860 race for president. This sounds like they were debating as presidential candidates. However, they were not. They published the text of their debates from the 1858 Senate race in Illinois. The first debate in the general election for president was in 1960, also the first televised debate.
The practice of active campaigning is older than debating, but for at least half the nation's existence, candidates did not themselves campaign. It seems quite possible that an incumbent could say something like "I'm going to concentrate on running the country. I hope you like the job I'm doing and vote for me, but this is a full time job that does not leave time for campaigning." They generally don't do this because they want to personally encourage turnout to win legislative races.
In general, the requirement to get on the ballot is to have your campaign collect and submit signatures. I don't think that there is any state that requires the candidate to appear personally. This is normally done by the campaign organization.