At least they think that they want to be famous but when they become so they find that there are drawbacks to being recognized wherever you go. Personal freedom and expression can be one of the first casualties of being known to thousands. Time is a commodity that is precious to everyone, but it is often demanded by admiring fans as something they have a right to access. I have worked in an environment that was frequented by many rich and famous people. More than a few either went by car everywhere so as to avoid the crowds or they had various forms of disguise in order not to be recognized.
People have limits on how much they want to be adored.
Jesus was alive at a time without the mass communication of radio, films and television. Telephones were not even imagined and writing letters was undertaken only by the wealthy on matters of great importance. Few could read and even fewer could write. Into this scene of slow moving events Jesus conducted his ministry and became so well known he was pursued by those people who wanted physical or spiritual healing. At the same time he was developing an opposition group who also came after him and pursued him as relentlessly as his admirers.