The neighbour is being incredibly reasonable. It would be nice to know what type of tree it is. Crown reduction work is specialist work. I have seen so many cowboy surgeons that have butchered trees. Trees want to do what they naturally do. If you hack the top off, they will be back at the same height in a short period of time but look worse and become more unstable. Some crown reductions will need future work.
For terraced housing, trees at the end of the garden can provide privacy from being overlooked. I sympathise that a large tree can cast shade. I have a neighbour with a towering sycamore that is now nearly spanning the entire width of my garden. Luckily I am on the sunny side of that tree. It's slowly squeezing out the planting in my garden, competing against my own plants and trees. It's a nuisance for me. It was however there before I moved in, and does provide a home for an abundance of wildlife. If I could actually get high enough to cut overhanging limbs, I still wouldn't bother because the proportions of the tree would be totally screwed and the tree would be deformed without careful limb work. The neighbour with that tree turned around to me and complained that I had too many trees. I removed three of them to let in light into her garden. I was then met with: but now I have less privacy. I have never asked her to remove her tree. Basically there is no pleasing some people.
Due to the nature of terraced housing and thin gardens I do think people should be mindful of others and be a little careful with planting. Some large trees that I cut back drastically (field maples), were back at the same height three years later. Trees want to be at their natural height, and for some specimens that's huge. I have moved to a pollard and coppice system for some of my trees, as it's more manageable for me. High canopy trees can sometimes let through light lower down, and today when feeling sunburn on my bonce from the day before appreciate shade when the sun actually shines brightly. So there's plenty to consider and lots of nuance. I did remark that I would need to remove one of my trees and was told by another neighbour that would be a shame as they liked it.
However both my current neighbours have hacked limbs off my own trees, not even cleanly and responsibly. And both sides have complete wastelands, that look terrible from my perspective. They only pull up plants, never plant, care or nurture. But that's my problem.
I do think you are being unreasonable, but you can but express your concerns, and the neighbour sounds very amenable by suggesting that they would be happy with works done even though that would be at your expense.
I have an Aunt that moved next to a park. And complains bitterly about the trees that line the park! Moaning that the council need to take them down. It's utterly ridiculous. I noticed one neighbour paid to get some thinned out even, I assume with council approval, and they have made a complete mess of them.