If people treat it as a free day off, then it sounds like the problem is not allowing working from home but a lack of effective performance management, or problems like that would quickly stop when.
Should I switch to high-touch performance management all the time for all employees, just because of the 1% of one person's time spent working from home?
I'm a strong proponent of allowing people to work from home, but I have also had conversations with people in the past about whether its appropriate for them. Ultimately it needs to come down to the question of whether people are getting the work they need to be doing done, and if not whether that's for reasons outside of their control. If people are delivering what they need to be delivering (whether that's in the way you'd typically expect or not), there isn't a problem. If they aren't delivering, that's the problem to solve, not the nuances of a work from home policy.
You think if someone is a good employee 99% of the time I should fire them on the spot?
If you know whether people actually delivers or not, this is an easy discipline issue: point out that you know, and that working from home is a privilege that will be withdrawn if performance slips.
What I tend to find is that managers often believe productivity is higher in the office because they see people engrossed in their computers, without seeing what people are actually doing, and believe they're in control.
If you think you need a high touch system to handle this, then it suggest you doubt your current systems ability to pick up actual performance vs. whether they look busy.