Yes, it is harder for renters, but it is designed to be harder. This is to prevent renters from having political power and making homeowner's houses more expensive. One more reason to fight, from my point of view.
A change of address is informing the government you moved and happens millions of times a year. Automating it doesn't just save citizens 10’s of millions of hours per year it also saves all the effort by all these different agencies when people communicate the same information to multiple agencies.
You have oversimplified the details of this sort of integration and conflated local vs federal institutions. The best way to do this change would be through your state's BMV/DMV, and many states already update your registration (or offer to) when you submit an address change there.
Registration and voting are easy and well documented in every state in which I've lived or researched.
It’s not that it takes a lot of effort per person to update the DMV and voter records it’s dumb specifically because most government agencies are automatically updated. So essentially this is just wasting 330 million peoples time for absolutely zero benefit.
https://www.vote.org/early-voting-calendar/
If people want to participate, they have many options.
I've found that if you need to argue edge cases (single parent, hourly schedule that almost completely overlaps poll hours, no absentee, no early voting or mail-in, and an employer that violates law) as you have in your post, you do not have a compelling argument.
1) Some people are under more stress than others, and are less able to summon the effort to vote. Admittedly, this does also include people in rather different circumstances, such as elderly homeowners who become unwell at election time (especially after the postal vote deadline).
2) Voting arrangements aren't uniform between countries (or even within one country), and travelling some distance to a polling station and then queuing to vote is a burden some voters might experience much more than others.
Further, you won't ever come up with a system that is 100% inclusive, secure, reliable, and economical. That should never be the goal since it's not achievable or necessary. Covering 99% of cases is good enough.
States in the US have more atonomy than states in most of the rest of the world. So much so that it often doesn't make sense to compare national US figures to national figures in other nations - education being a good example - https://learn.uvm.edu/blog/blog-education/vermont-eighth-gra...
But the same applies to voting. The federalist system under which the US operates allows communities and localities the flexibility to operate in a manner consistent with local needs and values.