States have been proven by experience to be willing to do both. AFAIK, all states that have implemented some form of voter ID to date collect fees for issuance of any eligible IDs. And there are numerous cases of states closing or moving DMVs and similar agencies, or mucking around with vote schedule, to deliberately suppress some voters (a recent example which is particularly glaring because the state explicitly admitted its motivation: https://www.snopes.com/fact-check/north-carolina-voter-id/).
Thus, the only way to ensure that voter ID would not be discriminatory in practice, is to have feds run the whole thing, in a way that guarantees non-discrimination - which means it has to be free, and it has to be easy to get. If you truly believe that voter ID is necessary for election security, then this is the compromise deal that you'll have to accept for us liberals to be onboard with that (keep in mind that most of us don't believe that there's any real issue to be solved by having voter ID, so any such support would be mainly symbolic in nature - and you'll have show good faith in courting it).
Wow, this is mind-blowing to me. A fair election is the basis of western democracy, a sacred institution. In my mind this pretty much equates to treason.
I don't know how these people can sleep at night.
In the end, you have to register to vote, and in most states you do so with the same agencies that make Identifications. Requiring an ID card to get a voter ID, or having it as part of your driver's license or state id isn't a horrible idea.
There's no reason for it to be a "federally issued id".