The pull-downs are a bit more than just good practice.
Each circuit in a L293D is what's called a 'half bridge' or 'push-pull output stage'. It basically looks like this:
PNP transistor on top, NPN transistor on the bottom.
- When the input is HIGH, it turns the NPN on and the PNP off. The result is a low-impedance path to GND.
- When the input is LOW, it turns the NPN off and the PNP on. The result is a low-impedance path to VCC.
Put one of those on either side of a motor, feed them opposite inputs, and you get something like this:
It's called an 'H-bridge' because of its shape. The picture above shows current flowing from left to right, but if you reverse the inputs you can make it flow right to left. Very handy for reversing motors, driving speakers, and other need-to-go-both-ways applications.
Thing is, if the input is somewhere between HIGH and LOW, both transistors can come on at the same time:
That's called 'shoot-through', and is Bad. At best, it wastes current and generates unnecessary heat. At worst, it shorts your VCC and GND rails together and things go all 'splodey.
The actual L293D circuit uses Darlington transistors, where the main transistor is driven by another one:
Transistors are baiscally current amplifiers, and most transistors these days have a gain somewhere around 100. That means sending 1mA into the base of the first transistor sends 100mA into the base of the second transistor, allowing 10,000mA (10 amps) to flow through the second transistor to GND.
Darlingtons are very sensitive to small changes in input and can throw a lot of power around.. the worst possible combination for a circuit that can have shoot-through.
The pull-down resistors keep the input pinned LOW until some other part of the circuit comes along and sends it HIGH.
When you void a product warranty, you give up your right to sue the manufacturer if something goes wrong and accept full responsibility for whatever happens next. And then you truly own the product.