I have long wondered, why don’t the Democrats have populists?

They do, to some extent. Sanders is the most visible politician from that faction of the party, but there are others.

The major obstacle to Democratic populism actually driving the party, though, is that the Democrats are the home of the intelligentsia. Even more than the "corporate" Democrats, the intelligentsia Democrats have the whip hand over internal party politics. That's all the people who make their living in the knowledge economy but aren't necessarily the capitalists - the academics, entertainers, media folks, journalists, and the like. They have enormous cultural power and capital that the working class lacks access to. Class analysis has always been a little muddled on where the intelligentsia land. They are not the capitalist class, but are usually far more bourgeoisie that proletariat.

For the populist faction to really drive the agenda in the Democratic party, the intelligentsia "class" has to lose control over the agenda. And that's not going to happen. There's already been a class war in the Democratic party, and the working class lost that fight to the intelligentsia class.

I keep coming back to this, but there is no clearer example of that than the Inflation Reduction Act. Originally, Democrats like Sanders wanted every Democratic policy in the IRA (the $6 trillion plan), and it included most of the pro-labor measures from the PRO Act. But once the BBB got into the legislative grinder, and the Democrats had to start prioritizing, the item that got prioritized above everything else was fighting climate change. Other programs either got dumped (almost all of the pro-labor stuff, all the child care money) or were given a super-short sunset period to game the budgetary impact (like the child tax credit) - but the climate change money stayed the largest piece, and was not at risk of sunsetting.

Climate change is a super-low priority issue for most voters - but it's a very high-priority issue for the college-educated progressive "intelligentsia" faction of the Democrats. So the Democrats landing on climate change as their biggest revealed priority in the IRA shows who has the strength in the party.