What's the problem with skylights?

Windows are harder to insulate than walls anyway, but the most important insulation is in the roof because heat rises, so skylights would leak even more heat than normal windows already do.

Your logic is solid, but their usage kinda implies the opposite (that skylights would make summers worse, not winters). That seems possible given the obvious dynamics of increasing the amount of direct sunlight, but based on a quick Kagi the overall effect is actually good for both summer and winter if used instead of windows rather than in addition to windows:

  Introducing skylights allows the total fenestration area (windows plus skylights) to be reduced from a maximum 20% of floor area to as low as 12% of floor area while achieving the same baseline average daylight factor target of 5%, and reduces annual heating and cooling energy use and costs in all but two of the 108 models with skylights analyzed. In other words, when different combinations of skylights and windows are used to achieve the same target daylight factor, the heating and cooling energy cost savings are almost always greater when equivalent daylight comes from top‐lighting (skylights) rather than side‐lighting (windows).
https://www.energystar.gov/sites/default/files/asset/documen...

Probably less good if you want to enjoy the view horizontally.

Cameras and screens. /s mostly

"fenestration" - I love that word!

Even better is “defenestration,” a fancy term for throwing someone out of a window.

A home with smaller windows is harder to sell so almost nobody builds homes with smaller windows just because they put in a skylight. Small windows make rooms feel smaller and claustrophobic. A skylight gives light but not a view, and large windows give houses a modern look, efficiency be damned. If you search for "modern house" all you see is walls of glass.

at low low cost of feeling like in cage.

Like, it's good idea for a warehouse, limited for housing, people want windows