That's a very good question. Inverterless DC motors have brushes, not a good thing in a long durability automotive motor, nor is there efficiency great. There's a class of motors knows as brushless DC motors, but these are really just a different name for PMAC (permanent magnet alternating current) motors with the inverter built-in. PMAC motors are generally substantially more efficient than Tesla's inductive motors, but it all depends where you operate on the efficiency map. At high power, they're much more efficient, but at very low power, inductive motors can actually be better. Tesla fits such over-powered motors that most of the time they run at a small percentage of their maximum power, and claims that inductive motors are actually better for this usage. This will vary between markets and application, as PMAC motors would certainly be better for autobahn use than inductive. Almost every other automaker is going with PMAC motors, in part because they're more power dense as well as generally efficient, and I suspect that Tesla will end there as well, at least for the front motor. Permanent magnets aren't cheap, though, and the Chinese tried to boost prices for rare earth magnets five years ago or so with export restrictions, so perhaps Tesla will keep walking their almost unique motor path.
Current inverters can be 94-95 percent efficient, and designs with more efficient silicon-carbide or gallium-arsenide transistors can reach toward 98 percent efficiency. Those aren't really in really mass production yet, but expect to see a switch away from silicon power transistors over the next five years.
