Mr Hamilton said this was an important check and balance in the system.
"Now voters can enrol at the same time as they vote or even in some cases after. This provides no opportunity for proper scrutiny of the roll."
The ability and enrol and vote at the same time was also creating an incentive for late enrolment and could contribute to declining enrolment rates and rising special vote numbers.
National recommended that only people who were enrolled before the advance voting window should be able to vote ahead of election day.
Anyone who enrolled during the advance voting period should have to cast their vote in the polling booth on election day, Mr Hamilton said.
The party recommended a shorter advance voting period of 10-14 days instead of 17 days.
Labour Party MP Jacinda Ardern said National appeared to be showing "extreme paranoia" around voter enrolment, and questioned whether there was something "more sinister" about their recommendations.
In response, deputy manager Cam Cotter conceded that he could not cite instances of electoral fraud in relation to their concerns, but he said that was not a reason not to remove safeguards from the system.
Electoral Commission figures showed only a small difference between the advance votes at the general election and the final result.
In the advance votes, National polled 47.85 per cent and Labour polled 24.49 per cent. In the final result, National won 47.04 per cent of the vote and Labour won 25.13 per cent of the vote.
Meanwhile, the Labour Party clarified to the committee that it did not want sanctions such as welfare cuts for people who did not enrol to vote - as previously reported.
President Nigel Howarth said the party's written submission had been "poorly worded".
"Our thinking was to create greater opportunity to enrol ... and to consider how the many points of engagement between the individual and the state night be used for that encouragement."
"We firmly reject any suggestion of a sanction imposed by the state in relation to state support consequent on a failure to enrol."
The party suggested that enrolment information could be included in change of address processes, council rates letters and student loan correspondence.