Monitoring butts-in-seats is a good metric for solving one kind of productivity loss. Eg - not doing job at all, the problem is that it doesn’t address the core issue of measuring what actually needs to be done.
As soon as your job involves thought work, there is rarely any connection whatsoever between where the job is done and productivity. For example, in software development it's common that NOT writing code right now is the best choice if you haven't done the other steps. For jobs like this, productivity is a cycle that involves first learning, then planning, then finally maybe writing some code. Or maybe learning some more first and then continuing to plan.
Planning is by far the most important piece, and it can be done literally anywhere and even while performing another task as long as it isn't a mentally-demanding one. So, at least in my experience you literally cannot plan while coding. Not anymore than you could write a novel. But you can do it while lifting weights, going for a jog, eating lunch, sleeping, taking a shower etc. etc.
Where's the most comfortable place to plan? It's okay for that to be answered differently by different people. For some people that's the office. For many more people it's sitting at home in pajamas or whatever.
Only if butts-in-seats is your company's output. Anything else, and you still have to quantify productivity by looking at output.
The only thing this might measure is time you are available to do work, but the same can be done remotely.
I am far less distracted by the random conversations people try to pull you into, or loud chatter of teams around me, when I'm at home.
I deliver so much more at home, though I do see some value in being in the office, I just find it frustrating how many people seem to rely on the office for their social life and also loudly take video calls from their desks all day now.
As a manager it would be your job to identify those folks and treat them accordingly. Arguing that "I can't manage remotely" is mainly an admission that you can't manage at all.