Sure glad Lincoln and others didn't share yall's thoughts back in the 1850's.
It's not the 1850's.
Back then, candidates were selected by party bosses or state legislatures because there were no actual primaries. You could not make a direct appeal to voters, and those party bosses clearly wanted to maintain their own power. Therefore, the only practical way to change the direction of a party was to start a new one. The lack of a primary system is why parties rose and fell in the 19th century.
But with the advent of primary system, the feasibility of third parties diminished because internal "takeovers" became possible. The direction of a party could be changed significantly just by a candidate appealing to voters directly. Since it was no longer necessary for a new movement to have a new party, voters and candidates simply try to win the battle for the party at the primary level. And if they don't, they generally conclude (rightly) that an independent effort would be even less successful. You'd have the same or even less (because some voters would stick with the party) support, and no organization to mount a national party.
Had Reagan run as a third party candidate in 1980, he and Bush would likely have split the GOP vote, and we'd have gotten a second term of Jimmy Carter. So if you want a conservative takeover, just take over the party. The only thing you really need is voter support, and if you can't get that...your third party effort would fail anyway.