What's wrong with paper? Single answer: Consistent recounts. For example, the US had two really high profile, narrow elections (2000 and 2020), and they still cannot figure out how many times to recount to believe the result. Best of 3 recounts? Best of 5? Keep recounting random places random times until the person you like wins? Does that even change or improve anything?
With paper, it's 100% guaranteed that "No two recounts will ever be the same". It's a human process. Two humans verifying it will never come to the same conclusion. One will say the "ballot stamp was not in the right place", another will say "chad did not fall off the paper", someone else may just be tired in the night, so on and on. As a democratic society, we have had large cases of recounts that it's not even a surprise anymore. It has become the go to whining and agitation tool for losers.
For the continued functioning of democracy, we have to put an end to this recount problem. If a winner wins by 1 vote, it should recount to the same 1 vote difference no matter how many times you do it. If not, elections are undermined (and thus democracy).
As for the "voting machine", people in this forum are really not good for judging as they think in terms of "modern" tech software with C or Python with a running OS. Read this thread for more info [0].
A good way to describe the voting machine, is a dumb printer. It originally exists to print a proper valid ballot for the elector who then drops it off. The machine just so happens to also have a secondary counter in it while it prints, so it can be secondary verified for extra safety. The paper is what matters and it's still there. This is called VVPAT, Voter Verified Paper Audit Trail [1].
Over the course of time, after many many recounts, it becomes obvious that the machine-printed ballot and machine do not ever diverge. So it just so happens that for convenience, the machine has grown to get counted first. If anyone has a doubt, they can easily go back and verify the ballots which are stored forever. It has been proven over and over to give consistent recounts and restore trust in elections.
Trivia: First time a Cabinet-rank senator in India lost election by 1 vote [2]. Recounts tallied down to 1. It has happened again. Chaos still did not break out. Candidates were not fighting over who was the winner. Reason? Voting machines and verified ballots. Recounts won't change reality.
I'll finally leave you with the summary of an excellent video on elections in India before/after voting machines. Every loser will complain and blame something. Hacking the voting process, obstructionism, who's issued voter IDs, where and how many voting centers are placed, gerrymeandering, media, pre-mature leading polls, on and on and on. All this thing about Voting machines is a classic case of shooting the messenger. The voting machine only exists to give one less reason to blame on. Don't shoot the messenger [3].
0: https://news.ycombinator.com/item?id=25106044
1: https://en.wikipedia.org/wiki/Voter-verified_paper_audit_tra...
2: https://en.wikipedia.org/wiki/C._P._Joshi
3: https://www.youtube.com/watch?v=zdo43a4JfYQ