The problem with replacing those lights with any recessed light is that you must first remove the electrical box inside the ceiling. It's much easier to use a slim, flush-mount light that can be attached to the electrical box. They're available in many diameters and depths. I'd use a 3000K model. Examples:

• DSE5 5 in. Round White LED Flush Mount Ceiling Light, 3000K
• DSE9 9 in. Round White LED Flush Mount Ceiling Light, 3000K
• 15 in. LED Flush Mount Ceiling Light Fixture
• Wafer 9 in. RD Integrated LED Surface Flush Mount 3000K

I had not thought of that at all, good grief, thank you!

In this style, though, it seems that the "bulb" is integrated, meaning, the fixture itself is useless once bulb burns out? Do I understand that correctly? While I wouldn't be using these as often as I do my kitchen cans, I have been surprised at how often I have to replace the GE Refresh bulbs in those.

"Do I understand that correctly?"

Yes, but the fixtures are so cheap and their service life so long I wouldn't worry about it. This Juno Jsbc Series 5-in Matte White LED Flush Mount is only $12 and has a five-year warranty (if more than 15% of the LEDs fail).

Before you buy, remove an old light and look at the quality of the drywall underneath. If it's bad, buy a light whose diameter is large enough to cover the mess.