I think the idea of suspending voting rights is less about "punishment" than it is about preventing those who have demonstrated that they're willing to make choices that we've agreed are harmful to other people from voting in ways that are aligned with their poor judgment.
In practice, I think most states with laws that suspend voting rights, do so as a form of punishment. That certainly seems to be the case with states that permanently suspend voting rights even after a convicted felon has served their time.
I personally think felons currently serving time shouldn't be allowed to vote. Suspending that right temporarily seems reasonable. That's not a strong conviction I hold though. I could be convinced that voting is a right as fundamental as the other rights we still extend felons while incarcerated.
Once a felon has completed their sentence I think they should have full voting rights restored. I also think they should no longer be considered a felon, to the point where their records are sealed once they've served their sentence. The idea of "once a felon, always a felon" seems counter productive towards rehabilitation and reengaging someone in society, and simply vindictive. In most states, being convicted of a felony comes with an automatic, unspoken life sentence of always being a felon, where the ostracization continues until they die. That doesn't seem healthy for anyone, let alone the person who served their time.