They will probably find a different way. I heard there are keys for 1 USD (someone was claiming that, i havent look it up). I dont really think this is the root of the smurfing on the ladder. As result this isnt the fix.
I do think this is a good idea, but it will take up many resources from the devs, who have to manually look at all the games. Just banning them wont really solve the issue. It will become a cat and mouse play between the devs and the smurfs. As result it wont fix the root of the issue.
I am not sure how this is really different to changing the current Elo calculation to something new (which is something you dont want to discuss in this thread).
Having the new Elo only hidden doesnt really make sense to me. People will still complain about unbalanced teams, based on the visible elo. So changing the Elo and make the new Elo only hidden doesnt seem to be a good idea.
The best solution is to just alter the visibl elo. Good new Elo calculations are already be posted in the following thread:
This would be really terrible. In the old system your rating was more based on the number for games you have played then on the your skill. A good player was winning most of his games for that reason and could be seen as smufing. Smurfing in the old system was not needed for these players, because the Elo rating was a complete disaster. Going back to that system would be really terrible.
There are much better new system posted in Analyses of the ratings - Spotting the issues. I suggest you to have a look at these ideas.