Let's start by looking around us. We see that younger generations understand Standard Arabic rather well, and have a much larger Standard Arabic vocabulary than earlier generations did at the same age. A cursory search suggests that cartoons have played a role in this; for example, Weyers 1999 shows that American students of Spanish improved their listening comprehension and used a larger vocabulary after watching a Spanish-language telenovela, and Blosser 1988 that Hispanic children, once they've mastered the basics of English, improve their English by watching more TV (although this does not seem to work below the age of 2). So parents are probably right to think that Standard Arabic cartoons are helping their kids learn Standard Arabic.
However – let's be honest – those same younger generations remain largely unable to write a grammatically correct paragraph in it, and normally speak in Standard Arabic only to quote prestigious texts or to parody TV presenters or politicians. This suggests that what they're gaining from it is limited to what Weyers 1999 identified for learners of Spanish: better comprehension and a larger vocabulary, but not better production. I don't think it's an exaggeration to say that, in Algeria at least, Standard Arabic is effectively a read-only language: everyone under a certain age can understand it and read it, practically no one can express themselves in it correctly or confidently. So, as an educational tool, cartoons have their limits.
But education isn't everything. Cartoons are one of the most secure domains of spoken Standard Arabic, right up there with news broadcasts, documentaries, and historical soap operas, and well ahead of teaching, sermons, political speeches, and interviews, all of which often use varying amounts of dialect. For younger children, unless their parents read to them, cartoons may well be the only context other than school and prayer where they regularly hear Standard Arabic (cp. Hamzaoui 2014), and in any case are one of the first contexts they learn to associate with Standard Arabic. Shouldn't we be asking how this affects their feelings about the language?