I guess I proved your point to some extent: I care less about accent errors than other mistakes, and just consider it a typo. But reading a completely unaccented text is hard for me, and I text, e-mail, and communicate online a lot.
In my experience, people are not foregoing them on purpose, except on capital letters, which is an heritage of AZERTY keyboards + windows (hopefully AFNOR keyboards catches on). Capital accented letters is the example to cite if you want an example of computer technology changing our habits: my friend Etienne (Étienne?) insists there is no accent on hist first name, but it makes no sense to me.
The point was simply that accents in French can change pronunciation, or at least change the meaning even if the pronunciation remains the same.