oh, for electricity we have a "transmission efficiency," but not for gas? And for gas, you calculate with the highest efficiency you can find for devices, but for the heat pump rather with the lower average? Interesting...
2.5-3 is not a lower average for an air-water heat pump... very few people pay a lot extra to install a larger heat pump than the heat calculation requires and, for even more extra cost, reduce the flow temperature to 28°C and have the pipes laid less than 10 cm apart... Then the outdoor unit is placed in permanent shade in the north, and you can be glad if you even reach 3 in a mild winter...
And andimann mentioned the most important point at the end. It may be the most noble to store gas, convert it into electricity in power plants, and then use it in heat pumps. But that is by far the most technically complex and expensive way. Especially since dozens of new power lines would have to be built or upgraded for that... the natural gas network is already there, nothing needs to be upgraded...
The engineer always has to weigh the technically best but also the most economical solution ;)
Like with underfloor heating and a flow temperature of 28°C instead of 35°C... thousands of euros are thrown out the window for a few percent savings, which does not pay off even over decades...