But you can carry less battery and fuel up with liquid fuel instead, so you don't have to carry all your fuel/range with you.
Believe me, I get the theory -- my company is responsible in one way or another for most of the EVs on the road today and I have to deal with "suggestions" from armchair engineers every day. Unfortunately there's no escaping the fact that the pure EV will be more efficient within its range (and this is unquestionably the vast majority of our driving).
The "motor always runs at peak efficiency" is strained, too, because you actually do have to vary the power to match the road load, or else you're cycling the battery (which both accelerates wearout and is prohibitively inefficient). It's not a coincidence that roughly 100% of passenger vehicles use mechanical transmissions.
Make a histogram showing your number of miles driven daily. A typical EV with 100-mile range will cover ~95% of the daily use for most people. Schemes to bring the EV from 95% coverage to 100% include series hybrid configurations, battery swapping, and fast charging. All of these systems add significant cost and complexity and they only buy you a few more bars way out on the tail of the histogram.
It has just been discovered that research causes cancer in rats.