EVs have no problem "starting" in low temperatures. You might not be able to draw as much power for the drive train as the pack is heating up, but it's not a primordial "fuel-air-mix won't explode" problem.
There is no "problem" to get around; you either risk your battery pack getting damaged or you have an active battery management system that regulates the packs temperature. That will consume power, no way around it.
Now there are some conflating issues we have to consider. Tesla recently disabled in a patch the sleeping modes of some onboard components, and this vampire load might be contributing greatly to the large loss of energy reported overnight. The other is the drivers mentality; you don't drive it to the point of 5% remaining and then fuel up, thats how you do it with ICEs. Instead, you just simply plug it in whereever you can. And frankly, if you are going to keep it outside overnight at very very low temperatures (thereby forcing the battery management system to expend energy for heating), plug it into a 120V. They can (contra to your statement) get enough power from even from a 120V to keep the battery pack (and your range) at least at the same level, if not adding range.
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A side remark: I very much think this is a complete non-issue. 90% of driving is commuting, it is decidedly not long-range trips. And then this is mostly an issue of infrastructure; if there were at least 120V plugs at every parking lot, you wouldn't ever have to worry about these vampire loads. Infrastructure, since we are at it, is of course a much much bigger problem for gasoline cars; think of all the steps necessary to refine oil into gasoline and make it available at gas stations. Driving an ICE across states at the time of their advent would not have been a particularly enjoyable experience due to the general unavailability of fuel.