Also having big-tent parties under a FPTP system gives voters more choice since you don't have major party machines shutting down the little guys but instead giving them a platform. Once Bernie Sanders worked out (better late than never lol) he was better off working within the Democratic Party than against it he almost made it to the White House, and his faction could quite conceivably win in 2020.
Party establishments always crack down on new movements, internal or external, because it threatens the division of power. Reforming a party is harder then starting a new one, which is why splits are common in politics. You know Bernie Sanders had to work within the Democratic party? Because FPTP
kills off third parties. You literally praise FPTP for supposidly giving voters more choice by giving an example how it forced a third party movement to merge with an establishment party - and thus lessening the choices. Even if Bernie Sanders had won, the amount of choices wouldn't have expanded; It would have been a choice between Berniecrats and Republicans.
You seriously think there are no backroom deals in FPTP? Have you paid attention to British or American politics in the last 100 years? It's precisely the lack of alternatives that enables internal factions to squabble, fight and work behind closed doors without any real influence by voters. There is a pedophile running for the US Senate and he's probably going to win because people do not want to vote for the only alternative option.
Primaries really do not solve that, as their influence is marginal at best. For one, it doesn't actually create alternative options on election day. If you challenge a seated politician and win, well, yay for your faction and booh for the supporters of the just unseated politician. They now have to vote for the party they dislike, or the candidate they dislike. And let's not forget that primary challenges are more exception and rule, and succesful ones are even more rare.