Voter ID laws are typically a discriminatory response to demographic change based on false claims about an epidemic of voter fraud. But unless and until they are ruled unconstitutional they are the law in some states, so instead of waiting for the law to change it's important to use the time between now and the election to make sure people people like seniors, students and the poor are registered to vote at the correct address, have the appropriate ID to get to the polls and so on. Delays on this might impact their ability to vote in primaries and would definitely affect their ability to vote in the general. While Voter ID laws can easily impose an undue burden (especially in places like Alabama where many DMV offices have been shut down in an apparent attempt to disenfranchise voters), we can use the time to help alleviate that burden and help people to get valid ID. After all, there's pretty much no downside to having a valid ID.
I do not really think pen-and-paper voting is going to solve the problems the US has. I come from a country where we do that (Ireland) and it is slow as fuck to count votes, although that's partly because we have a more complex electoral system than most US districts. Still, even in referenda (which are simple yes/no votes) counting them by hand is slooooow. Considering the number of votes people typically cast at election time (President, Congressional Rep, maybe a Senator, state officials, local officials, ballot initiatives, etc. etc.) counting the votes by hand would take weeks because you would have to start over for every race on the ticket. After all you wouldn't want to grab already-counted ballots for President to begin counting votes for a Senate seat in case the result turned out to be close and you needed a recount. So either you have to have a definitive result for each contest before you start counting the votes for the next one, or you have to start giving people a separate ballot sheet for every contest. Where I live that would runt o 40 ro 50 pages of ballot forms that had to be handed out to every voter. It would be a logistical nightmare.
Now I don't mean to dismiss the real problems with electronic voting. But the problem is not that it's electronic as such, it's the lack of transparency. I am not sure what can be done about this. We could switch to open-source software, but that can also be subject to bugs and is vulnerable to hacking. I can think of a completely secure method of voting using blockchain/encryption technology, but there verfiability comes at the expense of secrecy which would be an even worse problem. So while we should definitely reform our electronic voting standards, there's no solution that is guaranteed to be problem-free. People who claim there are technologically bulletproof solutions (whether simple or complex) are simply wrong.
I'm sorry to tell you that paper ballots counted by hand are just as subject to corruption as electronic voting - I remember one election in San Francisco not so long ago where a whole bunch of ballots box lids were found washed up on local beaches, and like most people at the time I didn't find the explanation very compelling: http://www.sfgate.com/politics/article/Scavenged-ballot-box-lids-haunt-S-F-elections-3302604.php
Also, people on the losing end of elections in the UK and Ireland still complain that the ballots were rigged even if there's no evidence, so no matter what the system is people will always claim that voter fraud is a problem if there is political capital to be made out of it, as Trump is doing. He may not believe it or even care, but he knows his audience is convinced it exists, so he says so to keep the flock together.
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