Let’s say all non-trivial natural gas usage (for simplicity) is heating, and due to heat pumps you could reduce energy required to 1/3 of the energy currently provided by burning natural gas (and at 100% efficiency)
you’re still looking at about 4 trillion kWh of energy/yr (possibly a month - hard to get good data) that would be needed to do that switch.
most of it during winter.
Germany currently produces a little over 500 billion kWh of electrical energy a year.
So to replace natural gas for heating in this scenario, Germany would need to produce 9x the electrical power it currently produces. Most of it during the winter.
And not having enough production would kill people.
It isn’t a matter of not having enough heat pumps or people to install them, that’s just the immediate road block if you individually wanted to switch.
It’s a fundamental economic issue that would require investment on a scale heretofore not considered outside of world wars. And maybe not even then.
Right now, we don’t even know of a storage technology that could even work at that scale, let alone what it would cost to do it.
And depending on which way climate changes go, the size of storage needs to be potentially arbitrarily large. The more uncertainty you have, the larger it needs to be.
Unlike a fossil fuel, we don’t have (essentially) arbitrarily large reserves we can pull from, it all has to be made and stored in advance by the same infrastructure that produces your normal production.