However, assuming one cannot change their vote, I disagree that there is more opportunity for tampering. Each count of the vote is basically a statistical sampling, and it should stay relatively the same.

Here in the US, all elections are handled locally, at the county level. If there is fraud, it's hard to detect the day of the election, so the fraudulent vote becomes part of the official ballot count. Sure, months later, poll workers, voters, and politicians can be prosecuted for election fraud, but at that point, the election has already long been decided. It's very rare that a real recount is held that becomes the actual result. It's easy for fraud to become the accepted results.

However, with a long voting period with daily rolling counts, there is more opportunity for scrutiny, statistical methods, recounts, etc. If anything funny happens, it will be easier to detect with more time, and prevent it from becoming the official results.