Because the problem right now isn't actually the economy at large. The economy doesn't really need to be stimulated. Select industries are being harmed by the pandemic in a big way, but it's not a typical recession. Many industries are still bomming, and If the pandemic were to disappear overnight, everything would come roaring back immediately. The stimulus checks, like many of the covid related efforts, were all about the appearance of doing something rather than actually being important.
It's a difference in the basic philosophies of the parties. Republicans see people are individual actors and politicians as elected leaders, democrats see people as parts of collective groups and politicians as representatives of those groups. Downstream from those viewpoints, Republicans see collective decisions made by the state as dictates, Democrats tend to see them as cooperative efforts. Republicans don't like dictating economic activity, Democrats like cooperative economic efforts. It's a perspective thing.
So when Republicans feel economic stimulus is necessary, it's typically going to look like "get money into the people's hands and let them do what they want with it" or "let people keep more of their money."
When Democrats feel economic stimulus is necessary, they're typically looking to spend that money on things themselves, because if the goal is to get money spent in the economy, they may as well be spending it on things they think are nationally important.
It would be strange for the party that sees themselves as pure extensions of the populace to focus on direct universal payments, because direct universal payments are admitting that the people know better what to do with the money for themselves than the government does. When Democrats spend money, they believe they're doing that for the people, so giving money to the people to spend for themselves is just adding an unnecessary step. Like, Andrew Yang in the primaries was pretty cozy with right-wing Americans for a reason. The divide between Republicans and Democrats isn't actually that Republicans are conservative and Democrats are progressive. That's only true in some ways, and is subject to change every generation. The divide between the parties is on a completely different axis.