"solution is blocked by nothing more than evil insurance companies "

Well that part is certainly true!

But it's not. There are plenty of other obstacles.

For example, unions. Specifically public sector unions. They're a hugely important part of the Democratic coalition. But they've generally been divided on single-payer. Which, given the impossibility of passing such a system without near-unanimity in the Democratic coalition, has been the death knell for single-payer state systems in New York and California:

In discussing the death of California's effort a few years back:

For instance, a major goal for the movement is to persuade more unions to join the fight. Although the nurses union is leading the battle in California, other unions are against single-payer.

“As trade unionists, we believe everybody should have health care, but there’s a big fear that we’re going to lose the benefits that we have,” said Chris Snyder, political director for the local International Union of Operating Engineers in Northern California. “We have our own health care trust fund, and we don’t want benefits that we’ve fought for for decades to be taken away or watered down.”

...with further discussion of New York's failure to have single payer:

Lack of union support is a major problem in New York, where Democratic Assembly member Richard Gottfried has introduced a single-payer bill in every legislative session for the past 30 years.

“What is keeping the bill from moving in the legislature is opposition from public employee unions,” Gottfried said. “They feel they have negotiated excellent coverage, so we need to convince them that the New York Health Act is as good or better than what they have now.”

levernews.com - A backroom deal to kill single payer

It's been a common theme. While health care unions might be eager to get Medicare for All, placing their bets that political leaders will increase rather than decrease health care spending, other unions have opposed it:

jacobin.com - Democratic party platform medicare for all unions

But it's more politically expedient to talk about health insurance companies, rather than obstacles that come from more sympathetic members of the progressive coalition....