But then you are just punishing those that actually pay taxes by making them pay more, while those who evade keep doing it. Also I doubt it would be possible, as raising taxes in the current economical and political climate is a political suicide.
Personally I think you just have the wrong perspective. Increasing enforcement to decrease tax evasion _is_ raising taxes. And affected groups will fight very hard against enforcement so I don't really see why you think that approach is somehow easier.
And you seem be talking about the elimination of tax evasion as if it's actually possible. Clearly it is not. The amount of tax evasion can potentially be decreased through policy and effort and we just need to decide how much we accept. Maybe the current level _is_ acceptable? In any case, some level must be acceptable. What level is acceptable to you?*
*This is a trick question. It's basically unanswerable without knowing the cost of enforcement (which increasing asymptotically as the amount of evasion goes to zero). But it is a reality that everyone should probably come to terms with.