Tax levels are high and tax are being collected. Governments aren't short of money because of tax evasion.
Tax evasion is not a top priority however you look at it... the argument sounds like "but think of the children" to justify things that are actually motivated by other aims and/or ideological reasons.
My country loses about €32 billions in yearly income due to tax evasion. That's the amount of money that could change many lives if used right. Instead we're cutting benefits to the poor bto reduce our deficit. Tax evasion is a top priority.
Another solution is to just increase taxes until you end up with €32 billion in increased revenue. An advantage is also that this solution is actually _possible_ (as opposed to getting rid of all tax evasion).
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.