Learn Italian: Le stampanti inservibili, le ho scartate tutte. - The unusable printers, I discarded them all.

No, it is strictly mandatory in this sentence. The lesson covers optional agreement with the relative pronoun che, but here we are using the direct object pronoun le to say "them". Whenever you use the third-person direct object pronouns lo, la, li, or le before a compound tense, the past participle must agree with them. Because le is feminine plural, the participle must be scartate.

Why does the Italian sentence use the pronoun le when it already mentions le stampanti inservibili?

This is a structure called left dislocation. The speaker moved the direct object (le stampanti inservibili) to the front of the sentence to emphasize it as the main topic. When you pull the object out of its normal position like this in Italian, you must insert a direct object pronoun (in this case, le) right before the verb to refer back to it.

Le stampanti is feminine plural, so why doesn't the adjective inservibili end in -e like regular feminine plural adjectives?

The singular form of this adjective is inservibile. Adjectives that end in -e in the singular do not change for gender. They simply change their ending to -i for both masculine and feminine plurals. So, for the feminine plural noun le stampanti, the adjective correctly becomes inservibili.