It's a trade-off that many USA states make willingly. Citizens have the right to vote, period^. It's not a "right to vote but only if you have an ID." Requiring an ID to vote, to me, is as ridiculous as requiring an ID to speak or practice a religion.

[^] except for the case of felony disenfranchisement laws, which I personally believe are a travesty

> Lack of such simple verification makes the potential investigations much more harder than they have to be

This can be argued for any hindrance to bureaucracy. On the balance you get a much more robust system, with fewer centralized fail-safes.