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.
If we believe in free speech and that everyone has the right to do what they want, why should we be afraid of being bullied about who we voted for? I would say more damage is done by hiding your vote, further I believe this is the real problem and hiding our votes is not the correct solution for it.
True, but if I had a counter that increments the minute I vote then atleast I as an individual can know it is correct and it can be easily shown everywhere else too.
Only if you assume nobody else is voting at the same time as you. So that isn't really any use.