In the US, there are a number of problems with the voting procedure, too many to count really, I think facing and addressing those issues would be far better than making voting compulsory.
When voting is voluntary, certain groups are incentivized to encourage or discourage other groups from voting. This manifests itself as bribery, legitimate "get out the vote" efforts, making the process of voting difficult and so on.
Basically you've created an incentive for such practices by making voting voluntary. All of that goes away when voting is compulsory.
I'm reminded of the Spce Shuttle Challenger disaster in 2003. I saw a TV show about the investigation into that. After launch there was concern about the visible debris coming off the shuttle. The investigation afterwards showed that there was significant resistance within NASA to investigating that prior to re-entry. Certain people wanted to use satellite imagery to see if there was any damage to the shuttle. Other groups resisted.
The reason this was contentious was that such practices weren't required. The solution? The investigation resulted in NASA instituting a policy requiring such imagery be taken of all shuttle flights.
Once something is mandatory, all sorts of incentives (and the problems they create) simply go away.