In a car with normal port injection or even a carburetor, the fuel is mixed with the air in the intake. This means that the intake valve is "washed" with fuel as it enters the combustion chamber. Gasoline is a pretty effective solvent, so this helps to keep the valves clean.

I'd take issue with your premise though, because "modern" DI engine designs don't have the same issue with carbon deposits. The problem with early DI engine designs is that they simply took regular port-injection engines and converted them to DI without making enough adjustments to other systems.

You have to take a step back and understand how/where the carbon on the intake valves comes from in the first place. Carbon deposits don't just form from air; there has to be a hydrocarbon present. So where does that come from?

When your engine runs, some of the pressure from combustion makes its way past the rings and into the crankcase. This pressurizes the crankcase, which will push oil out of the engine. Not great.

So we need to vent this somewhere. If we vent it into the intake, we can burn it as part of the combustion process. This system is called positive crankcase ventilation (PCV).

Problem is that blow-by isn't the only thing that gets sucked into the intake. The oil in your engine is hot, so it off-gases hydrocarbons. This oil vapor partially burns when it hits your hot intake valves, forming carbon deposits. No problem if you're spraying those valves down with a solvent (gasoline) as the engine runs. With DI, you no longer spray the valves though... Uh oh.

So what's an engineer to do? The most common fix is to design better PCV design. Rather than a small canister style oil separator, most modern PCV systems use elaborate chambers for air flow that allow vapors to condensate and separate out of the air before it is drawn into the intake. Some even use centrifugal or cyclonic separators.

Another common approach is to mix both DI and port MPFI (multi-port fuel injection). Most of the fuel is injected via DI, but a small amount is sprayed in the intake under specific conditions. This keeps emissions down, but also cleans intake ports.

Modern engine oil requirements have also been adjusted to reduce vapor volatility. API SP, for example, is a very common requirement for DI engines, and this standard requires reduced levels of SAPS and lower Noack volatility scores.

That said, some manufacturers don't seem terribly interested in fixing the problem, so your statement is partially true. VAG used dual-injection on EU market EA888 Gen3 engines, but not in North America. Then, with the EA888 Gen 4, they dropped dual-injection globally (WTF!?). Honda, shockingly has refused to fix common engines like their J35Y8. GM's TurboMax found in their trucks lack good solutions to intake buildup.

Ironically, one of the worst early offenders, BMW, have pretty much solved the issue across their entire line. They use dual-injection, along with other mitigation strategies.

All of this is to say that you can't really generalize about DI engines these days, because there is a huge amount of variation in how each manufacturer builds their fueling when DI is present.