Don't fool yourself, though.
Accents are there for a reason.
Orthography influences pronunciation. In time people will start pronouncing those words as the orthography suggests rather than deducing it from the context.
Even if only because the context won't be discernible. But, generally, because of the principle of the lesser effort: it's always easier to just read what is there than thinking which pronunciation applies.
Eventually, the words will become homophonous (edit: assuming there are other words which differ only in the accents) - you'll effectively loose the words or they'll change, probably for worse.
The language will become more ambiguous and more dependent on the context knowledge - which will be hard to get if you don't know the language well to begin with.
In other words, you've just made the language "harder" to learn.
So, in effect, it's not a simplification at all.