I know some people used to chop down trees to get a line of sight for satellite TV. Starlink is different in that you need more than a single LOS to a specific spot in the sky, but I wouldn't be too surprised if a lot of people ultimately chop down more trees to get access.
Alternatively, perhaps the starlink antenna could be mounted on a large pole or modest radio tower. That would be ugly but probably a lot less ugly than chopping down your trees.
Yeah, I have a house in a heavily forested area. I put the starlink dish on top of a 12ft pole mounted on my roof. I have a double of line of sight issues, but it's good enough that I don't notice service interruptions.
For a house in the Adirondacks in upstate NY (heavily wooded), we used a 50' triangular antenna tower with Dishy at the top to clear the tree line. Went from abysmal DSL speeds to ~100Mbps, also added microcells from the largest mobile providers to improve cell coverage on the property (mounted to the antenna structure in water resistant housings). Total cost was sub $5k for everything mentioned.
If close to the home doesn't work, depending on siting requirements, you can erect a tower in a clearing or where there is clear line of sight to the sky and then run power and network to the tower from the nearest structure. Don't neglect lightning surge suppression to protect equipment.
Alternatively, perhaps the starlink antenna could be mounted on a large pole or modest radio tower. That would be ugly but probably a lot less ugly than chopping down your trees.