Fuel injection systems in vehicles seem to work pretty well, over a very wide range of flow rates, don't they?
You might think so ...
Some early (crude) petrol injection systems did run the injectors with a variable flow rate - no valves, just vary the pressure. These basically do little more than dribble fuel (petrol) into the airflow - and rely on engine heat to evaporate it fast enough. No such system could come close to meeting current emissions standards (for a road vehicle) as the fuel tends to be still relatively large droplets which burn off leaving a tiny carbon core that goes out the exhaust as soot.
All modern petrol systems run a high pressure rail, with computer controlled solenoid valves to open the injector for a variable time. The high pressure promotes atomisation and cleaner burn.
Similarly, diesel systems have developed. Even old ones used timed valve opening (mechanical valve internal to the injector pump). You may have heard of "spill cutoff" in relation to diesel injection - internal to the pump there's a piston that provides the high pressure, and a spill valve that allows it to go back into the fuel feed. At the start of the injection cycle, the spill valve closes, and the high pressure fuel is then forced to go via the injector.
But again, no mechanical system can meet modern road vehicle standards, and AFAIK everything these days runs a high pressure rail and solenoid controlled injection. But unlike petrol, the diesel injectors contain their own cam-driven pump which allows mind bogglingly high pressures to create the atomisation needed for clean burn - diesel, being a much heavier fuel doesn't evaporate nearly as well as petrol.
Not that I've converted anything modern enough to go down the injection route, but when adding LPG to a petrol engine, choice of injector (or rather, nozzle size) is a bit of an art. If the metering nozzle is too small, you reach 100% open before full engine power and you have an engine that's weak at high power. If the nozzle is too large, control at low power becomes tricker as a tiny change in opening time creates a large change in gas flow rate.
Back to your boiler ...
In principle it would be possible to on-off modulate an injector valve - but I don't think it would be worthwhile. In a car or lorry you are wanting sub-second timing, but in a boiler you generally aren't bothered over periods of minutes. The extra complexity (and noise, the injectors actually make a fair bit of noise) would more than outweigh any benefit. And there's a risk that well running at lower powers, you don't get the combustion chamber hot enough for a clean burn - promoting sooting up.