I agree with your opinion of bitcoin appreciating in price if it is adopted as a legal currency. But I don't think it would eradicate black money completely from the economy. And it is not easy to make bitcoin a legal currency.
Once governments remove cash, and I predict this is going to happen faster than most people are predicting (look at Sweden to have a look in the future...) the entire black market economy is going to be running under bitcoin, since bitcoin is the only realistic alternative. Everyone will start working for bitcoin, and getting paid in bitcoin, and this is how people will completely circumvent the tyrannical governmental control we are heading towards.
This is unlikely to happen
At least, in massive amounts. Bitcoin is nowhere close to being a realistic alternative. If paper money is no longer accepted anywhere (this is a big IF in itself), real life criminals will be trading with gold and silver coins. Bitcoin, with its transactions perpetually imprinted on the blockchain would be beyond consideration for genuine gangsters. In any case, you will have to exchange to coins to fiat and withdraw it sooner or later, and that's where you end up caught by police
More and more people are talking about a financial reset happening soon. I used to not believe in that, but look at India, Venezuela, United Kingdom. 500EUR banknotes are not accepted anymore in most European countries. Bitcoin could be an alternative: if any currency fail, it skyrockets (its demand, price, everything) in a few minutes only and will only keep rising, together with precious metals.