I feel you don't understand my major point.
Historically, US elections operate on the principle of coalition-building. Where a European politician builds his coalition AFTER he wins the election, an American candidate builds the coalition BEFORE the election.
In a coalition you need to have both the members of the moderate and the radical groups placated to some extent. THe moderates are more plentiful, but radicals are more likely to turn out and volunteer, vote, etc. Nowhere is this more obvious than in a campaign like Rand Paul's, where a large proportion of the funding comes from radicals.
While it is necessary for a candidate to moderate his message (something I think Paul Junior is doing with some success), if a candidate, especially one like Paul Junior, deliberately snubs his radical base to the point that they leave, he may encounter other problems. Do you think Obama would have won without the support of the Kos Kids?
There's always a Scylla and a Charybdis to be bested.