Well, it varies by country I guess.
Sure, but not as much as you think. This is why there is a whole field of study called Politics (or Government or Political Science depending on the label). And, that field isn't just area studies. I and other political scientists can tell you about the effects various systems are going to have. Those aren't determinative -- as I've indicated in other posts they depend, inter alia, on the underlying distribution of political preferences in the electorate. If 80% of the electorate wants an extremist party, you're going to have an extremist party, regardless of political system, to take a hyberbolic example.
There are also other things at work, such as primaries, local norms about the distribution of seats, availability of funding, and federalism that make the general, tinkertoy findings I've mentioned not 100% accurate.
What IS for sure is two party systems are extremely resistant to change. Any change other than to the other party is resisted by the full political force, to get them to lose their deathgrip requires practically national collapse before they are at any risk.
I know of no evidence to support this claim. It's surely the case that any entity in power wants to continue holding power, but I know of no reason why partisans of party A prefer to surrender authority to party B rather than party C. Unless, that is, party B is closer to them ideologically. We know that a given political system will tend towards 2 parties. There are good strategic reasons for that. What the identity of the two parties are is totally up for grabs. And, in the US, earlier in its history parties shuffled around a lot. The Republican Party, for example, was created whole cloth.
Now, there are good reasons to expect, especially now, that the Democrats and the Republicans will persist. They have a lot of resources, well-established brands, etc. And, despite the current clamorous political environment in the US, most issues are at the margins -- there isn't something like slavery dividing the nation.
But, even then, there have been major, I repeat
major, partisan realignments. So, while the labels haven't changed, the parties chose to radically change themselves. 60 years ago the entire American South belonged to the Democrats. Completely. 100%. And, the Democratic Party by opting to support the major Civil Rights Acts changed that. One could very reasonably argue that you had 2 parties, the Democrats (pre-1960s, and some studies separate out the Southern Democrats for just this reason) and the Democrats (post-1960s). And, their membership changed to reflect that. Strom Thurmond, to take a notable example, was once a Democrat. I believe the Republicans had a similar realignment, though it finds its way into fewer textbooks, involving their decision to embrace Evangelical Christians as a political force.