"In 2022, the Egyptian authorities allowed more exits of people through their border. The 144,899 exits recorded during the year are 44 per cent more than in 2021, representing the highest figure since 2014."
That's 6.6% of the gaza population travelling out of gaza per year, higher than the percent of Indians who travel abroad each year. This statistic also doesn't reflect the hundreds of thousands of exits from Gaza to Israel each year.
The "open air prison" is a lie. You can impute whatever motive you want to them leaving. I'm sure escaping Hamas persecution was a part of it for many of them. Israeli prosecution wasn't really a thing and the "mowing the lawn" narrative is propaganda.