With no combustion required, no heat is building up, as it does with internal combustion gasoline engines. This is why many electric cars can operate past 10,000 RPMs, a level of performance that would normally overheat and fry all but the most performance-oriented combustion engines.
There’s also another reason why electric cars don’t have multi-gear transmissions: it would add on additional weight and increase production costs. Considering that many electric cars already have batteries that weigh in at over 1,000 lbs, carmakers are constantly looking for areas in which they can whittle down their vehicle’s curb weight.