https://ballotpedia.org/Voter_identification_laws_by_state
Most states also have some kind of hardship waivers to help people get a basic government Identification since it's kind of hard to do a lot of things without some form of ID. Some states even have a specific "Election Identification Certificate" process that can only be used for the purpose of voter identification and it's free to get.
Hardship Waivers for IDs in Pennsylvania[2015] http://sharedprosperityphila.org/documents/Revised-ID-Waiver...
As far as the time investment required to get an ID to vote; if a person isn't willing to spend some time to make sure they can legally vote, do you think they will spend the time to make an informed vote? It's a pipe dream but I would prefer that everyone who votes does so while making an informed decision about who/what they are voting for.
I also support voter ID just because it makes it a little bit harder for foreign agents(A US state vs State example: https://edition.cnn.com/2018/10/16/politics/beto-orourke-con...) to interfere with what should be an internal affair. Although with political action committees (PAC) being a thing and with how hard it is to know where the funds are coming from, it's basically a free pass to have unknown monetary funds being funneled to politicians with questionable moral integrity.