So, at least for the Presidential election, there's a lot of reason not to do this. It'd also probably be bad to have the counter increment in a voting place when you submit your ballot, because then you would see how the person in front of you just voted, which we don't want, so people aren't bullied about how they voted.
And finally, technology does not actually solve problems: It trades problems we have for new and potentially bigger problems. For instance, if you are reliant on a digital system for counting votes, it is easier to tamper with and harder to verify that tampering has occurred. This is why if you want to be sure your vote actually was counted correctly, you should always vote on a paper ballot if it is offered in your district.