In USA, voting registration requirements are up to local laws. If they're complicated in your area that's because the people in charge want it to be complicated for you. That's frequently the case in order to reduce the 'wrong' people from voting as most of those people would vote against the current people in charge.
What does the eID change here ?
A digital ID in the USA would mean every company would ask for it when you sign up for random services. That way they'd know your real identify and could successfully block and ban you if you break their ToS or just don't want to do business with you. You can always lie about your name, birthdate, and can get new emails address or phone number. You can't get a new government id on a whim. While that might sound great for removing trolls, a lot of these service bans are from user submitted reports. You can go on most platforms and submit a bunch of baseless reports against a target to get them auto-banned. A ban from Google could break your email, your phone, your tables, Google Docs, your online photos, etc... A ban from Microsoft could kill your local PC and risk losing access to all your files on it (TPM linked encryption linked to your Microsoft account). Etc... Further, anything you said in the past will now be linked to your identity since that account will be linked to your true identity. Said anything about Charlie K six years ago? Now people may harass you for that comment, get your work to fire you, etc... Any mistake or embarrassing thing you've done will follow you forever. Linking your speech to your identify greatly suppresses what people say. It doesn't change how they feel, it changes how the present themselves. For a society to function well, it's important to know how people actually feel about things.