The people who vote in primaries aren't all the people who vote in general elections.
So because the political opinions in primaries skew to the left or the right, nominating a super left (or super right) candidate will generally result in that candidate being beaten in the general. People will vote for a candidate that is the closest to them ideologically, typically (obviously things like charisma matter too). So in a red state, you need a centrist Democrat to even have a chance.
See: Todd Akin, Richard Mourdock
Again, I think the main issue with this is that voters don't see "left/right" in the same way as political pundits do. I'd argue most voters (
especially the people who don't identify as part of an existing party) don't necessarily even think in those terms in their day to day lives.
So for example, is a candidate coming out and saying they're actively opposed to corporate influence on politics (and works from a grassroots level to build support that doesn't depend on corporate donors so that they can credibly sell that message) automatically a "leftist"? Opposition to most modern free trade deals was largely seen as a "leftist" view, yet that was one of the (very few) planks of the current Republican President's platform that mostly stayed consistent since he first started campaigning, and Republicans are
now largely against them as well. Is Trump a leftist now? And of course, as you already pointed out,
partisanship and individual candidates can have a strong hold on people and affect what kind of issues they end up supporting. Clinton was considered further left on guns in comparison to Sanders, but did the people who supposedly hate "purity tests" make a big deal over that how that would make her lose a general election? Sometimes a majority of Americans
support something like single-payer healthcare, and sometimes a majority of Americans
don't support it, depending on how the issue is framed, and the person making the case. School vouchers, previously considered another Republican privatization idea, are now
supported by plenty of Democrats.
So the liberal/centrist/conservative/left/right divides are useful in some respects, but I'd caution against thinking these are 100% set in stone categories with no variance. So Democrats should stop thinking anything outside their mainstream views is automatically some communist purity test position that will automatically scare away voters.