> This is not acceptable

Why? I'm a software engineer working in an agency and I work exactly like you're describing. If I feel like going on a run, I'll mark myself as AFK and go on a run. If I feel like closing my laptop at 3 and go shopping, I'll work later in the day when I'm not busy.

I still deliver on my deadlines and contribute more to the company than most colleagues. If you ping me on my phone I'll probably reply at any given time, and I put emphasis on written communication about issues I'm handling. Ideally, I've already written down all of the information you'd want to talk to me about.

This "style" works really well for me.