Electric motors can achieve FAR greater than 1kW/kg. Here's one used sometimes on electric aircraft capable of 10kW/kg, same as a jet engine: https://emrax.com/products/emrax-268/
The specific energy of lithium-ion is poor, but jet fuel's USEFUL specific energy is more like 10-15MJ/kg due to needing to be burned. There's also some efficiency improvement possible, i.e. from airliner lift-to-drag of 16-20 (and like 8-10 for a Cessna) to a more glider-like L/D of 25-35 (the best gliders can do 70). Additionally, improved modern materials means you can just have most of your take-off mass be battery, compensating for the poorer specific energy (general aviation craft are only like 10-15% fuel, but 777s can be almost 50% fuel, and electric aircraft could be 60% battery).
So if you combine efficiency improvements and high battery mass, sure, electric planes still may have a tenth the range of jet liners. But jets like the 777 have a range of 10,000 to 15,000km. A tenth of that is still over 1000km! Quite doable for a very large portion of domestic flights. Since domestic flights often involve multiple hops anyway (due to hub and spoke model), you could fly basically anywhere up and down the eastern seaboard in just the typical two hops. And faster than high speed rail.
But of course, there are already better lithium batteries that are available in small quantities, like lithium-sulfur, metal electrode lithium batteries, solid-state batteries, or batteries that combine those various features. ~1.5MJ/kg cells are already demonstrated and you can buy them on an evaluation basis. ~2MJ/kg is feasible as well, enabling single-hop flights all over the eastern seaboard and enabling multi-hop transatlantic flights (as low as 1200km is the minimum range needed for transatlantic flights if you really wanted to do it).