So you're spending ~$80 per year for DO plus $180 for the hardware. Over 5 years that's $580 (if that Chromebook really makes it to 5 years and DO's prices remain unchanged). This is about half of what you'd have to spend on a local dev setup with similar capabilities.
Not bad, but I think whether or not it makes sense depends entirely on the productivity difference between the two setups.
I started working like this in the summer of 2017 so I'm right at the 5 year mark with this setup (I actually need to get a new device and DO's prices have remained the same - I think they've actually gotten cheaper and I'm on a more expensive plan - $5 vs now they have a $4 option).
Due to my client work, I need an online test server so I'd be paying for a test VPS either way.
Being able to open my Chromebook and tmux into any project in about ~15 seconds provides enormous productivity gains for me. Not sure if I mentioned this previously, but I'm a freelance developer and sometimes juggling 6-8 clients at a time so being able to pull up any project at any time from any device with SSH access is very powerful for me.
Not bad, but I think whether or not it makes sense depends entirely on the productivity difference between the two setups.