I can relate to this. Admin job at the council. I could do the work I was set in less than an hour, yet had to sit there pretending to look busy for 7.5 hours per day. I started off in a small office with 2 other admin workers. No one kept tabs on us, and I actually wrote a novel during the 3 years I had to sit there with no work to do!! I lost count of the number of different jobs I interviewed for and didn't get - but then how was I supposed to move up the ladder when the job I was in was gave me no valuable experience?!
After a restructure we got moved into a huge office with a new manager. Over the next 2 years, I repeatedly raised with him that I could take on more work and was thrown scraps here and there, which filled a few hours at most. Many colleagues made noise about how "busy" they were. I frequently offered to help but everyone was protective of their workloads. I came to the conclusion that either a) they were hugely inefficient or b) they had very little to do either but were afraid of making themselves look dispensible in light of looming redundancies.
By this point the job wasn't just unfulfilling, it was soul-destroying. The new manager monitored the minutiae of our office movements and then tried to bring a disciplinary against me for personal use of the internet in work's time. I asked him how he expected me to use my time if he refused to give me enough work to fill the day?! He just couldn't comprehend that they were cause and effect of the same issue. I told him I was worth so much more, walked out of the office and never went back. I subsequently got signed off work, negotiated a voluntary redundancy payout with HR, and started a full-time Masters degree.
That was around 15 years ago. Since completing my Masters I've been self-employed, doing creative, fulfilling work that I love. I wouldn't change my job for the world, but bloody hell, I earn every penny of it and then some!
OP, I'm actually surprised that jobs like yours still exist. My understanding (in the public sector at least) was that cost-cutting exercises had got rid of most of these redundant roles.
I wouldn't say you're unreasonable to do almost nothing at work - it's not like you're actively avoiding tasks, or letting anyone down, is it? There's an end in sight, so use that time to learn a skill online, as long as you don't have a horrendous manager like mine breathing down your neck!