Maybe I’ve seen my HOD and how they work, and feel like it’s not the most difficult role, but what I should consider is the school I was looking at is double the size, and it will mean more staff in the team which means more workload if I was to take on a tlr.
If that is what you believe you need to open your eyes a bit more. Perhaps it's because I've been in a core subject for so long, but there is so much hidden work going on behind closed doors I really feel you underestimate how much time is being consumed by this at barely any extra protected time.
-currciulum design, mapping, tracking across every member of the department and for every year group, often several times during the year as circumstances change
-data gathering, tracking, analysis, evidence of continuous improvement
-responsibility for ongoing internal staff training, often weekly
-responsibilty for every staff member in your department - their fuck-ups are your fuck-ups and someone will almost always take up 80% of your time on this
-go-to for each of the following: cover when a member of your department is absent (both setting and doing), parental complaints and questions, staff questions on every aspect of their role, school-wide subject links, trips, authorisation of just about everything from budgets to absences
-ultimate line management responsibility, no matter how well this might be divvied up, you will still be required to know everything
-budgeting - current and forecast, keeping on top of how much your staff photocopy, your inventory and new orders
-behaviour in the department - guess who will take on the kids kicked out of classrooms and who will be responsible for holding internal detentions, centralised or not?
-keeping up to date with changes in the currciulum, Ofsted and the school culture and the dissemination of all this to your staff (some of whom will, inevitably, not play by the new systems)
-extra meetings for department heads, representation at every event from options evenings, asslemblies etc. to every results day
-Ofsted
-often an expectation to hold after-school and holiday revision classes
I'm sure there is more that I've forgotten, but even if you're paid 10k more for the priviledge it's certainly not much given tax, pension and the amount of hours worked. It's not an easy job and much more difficult than you seem to imagine, no matter how big the team is (and having a smaller team brings its own issues, especially if someone leaves and cannot immediately be replaced).
I have a (now ex-) colleague who has just accepted a HOD role. They won't last a year; they are way too lazy to do the job this entails, let alone the people skills this needs, but I'm sure they thought it wasn't going to be too difficult, either.