More on our specific build just in case that changes the thinking.

2200-ish square foot ranch home with 9 foot ceilings. Fairly open concept. Family room has a slight vault to it (trusses overhead, so there's plenty of room), but everything else is flat.

Recesssed lighting to be in study, kitchen, hallways and family room.

I am not a lover of intgrated lighting since the ability to actually replace a bulb is IMO a big deal. I see nothing wrong with 4" pots and LED 4000K bulbs in almost every space they can be on a dimmer in places where you want that but when a bulb dies easy to replace without replacing the fixture. LEDs do not last forever.

When the position of the can is critical, I'd recommend remodel cans even for new construction. Run wire, drywall, drill exactly where they go, fish for wire, and connect. I've seen too many cans installed halfway over a full-height pantry cabinet and not centered over the doors.

I used Juno 17* trims (scroll down for the many finishes) and compatible housings (e.g., Juno IC1, TC1R) in my living room upgrade. The trims are also available square. I wanted fixtures whose bulbs (PAR20) were recessed to reduce glare. I used these 2" Nicor DLR2 in hallways because I wanted small fixtures there.

Note that recessed downlights with screw-in bulbs aren't legal in California (see page 6-6).