The early shop-around dynamics on the Republican side have really been fascinating to watch, haven't they? For my entire lifetime, the GOP has ultimately gotten behind the next person in line, the establishment candidate. Ronald Reagan, George Bush I, Bob Dole and George Bush II all had their primary scares, but they did won the nomination.
Compare that to the Democrats and their willingness to turn on Ed Muskie or flirt seriously with Gary Hart or never have a bona fide establishment candidate to begin with. Remember when Bill Clinton had accumulated enough delegates to secure the nomination in 1992, but still suffered talk that the party would find a way to dump him in favor of Bill Bradley or Sam Nunn or somebody like that?
Update: Much other commentary made the opposite assumption, that Thompson wanted to get word out about his illness ahead of his announcement of candidacy.