Though I've never used any time cards before, I imagine that it's a good way to keep employees honest. If you trust your employees to keep good time, you can just have them write up their own time into excel or something. I've always done my own timesheets everywhere I've worked.
TheoPetro hit some major points. In order to have software do the same thing as time cards, there'd need to be some way to authenticate the employee. They'd need to sign in and enter if they're leaving or arriving. This could be an even bigger hassle for the users. Adding hardware like cards or trackers would make it easier, but increases the cost.
Maybe it's just a matter of improving the current process of calculating the hours. Instead of totaling all the hours in 1 session, do it every few days. With time cards, it's not like you can go back and change your time so there shouldn't be any trouble totaling them immediately afterwards.