I think that going state-by-state was smarter because although the effects would not be as widespread, it would be easier to obtain the result desired of obtaining the right to vote. It would have been very hard to get the amount needed (2/3 of all states) to obtain the amendment with no prior suffrage laws. Some state governments were not very inclined to let women vote, so this was a huge barrier that could be somewhat bypassed by just going one state at a time
