Centrism isn’t even more “pragmatic” than leftism. The “market based solutions” that centrists offer, e.g., the Affordable Care Act, are almost always failures in comparison to state run universal programs, e.g., the NHS. The only thing halfway pragmatic about centrists is that they’re willing to sacrifice their ideals (if they have any) for symbolic victories. The far right, meanwhile, has learned that centrists are fucking spineless suits that they can walk over with no resistance.
The GOP has been ideologically intransigent for the entirety of Obama’s term, and the centrists in Congress have offered zero resistance. It was the progressive wing of the Democratic party that made the most waves in fighting against a reactionary GOP, but it was the progressive wing that was thrown under the bus to protect shitty right-wing blue dog democrats who ended up losing their re-election bids anyway (like my former senator, Mary Landrieu).
Most progressive policies have widespread public support. More people are for more strict gun control than are against it, more people are for a single-payer public option than are against it. If centrists ran on a left-wing platform, rather than vouching for complicated “market based” policies that appeal to other idiot suits comfortably sheltered by think tank executive summaries, they might win some fucking elections. But that would require them to drop a pseudo-realism and pseudo-rationality that has dramatically reduced the power of left-wing lawmakers and empowered the far right.