There is no need to avoid useful words, even if they are used often. The problem is with words that don't change what you say while making it longer.

There's some use to most restrictions you can put on writing, simply to break old habits and grow. Not every change is an improvement, but every improvement is a change. I meant it more as an exercise than a rule (which is why I said "might be interesting...").

Or it might be useful to do te exact opposite: analyze your writing to determine where you are using obscure words when there are common words which mean the exact same thing.

That is not quite the exact opposite, as they draw from different corpora. Both would be interesting and quite possibly useful.