This isn't why we don't have online ballots. The issue is specifically that you aren't in a voting booth, which means there is no control over voter influence.
Imagine a husband and wife plus a ballot initiative on outlawing flowers. The husband is strongly pro-flowers while the wife is strongly anti-flowers.
With online voting, the husband or wife can force the other to vote in front of them. There is no plausible deniability, so individuals are easily pressured into voting one way or another. Groups can say, "you need to vote in front of another group member" to pressure everyone to do what they want.
Voting booths prevent this, to a large extent.
Another issue is electioneering. By current law, one cannot campaign within 100ft of a polling station. This gives a "safe-space" where people can think about their options and make up their own mind. If I can vote on my phone, a random volunteer can get me all hyped up on the street and I can impulse-vote on the spot. Not a great way to run a nation.
(I'm not saying the current system is perfect, or anywhere close to it.)