Welcome to the forum.

Wall T-intersections: If a wall meets another in the middle, and not at an end, I can't join them. Part of my design process is to slap down a bunch of walls based on a napkin-quality sketch, then resize things as needed. (Oh, this corridor is too narrow; I'll just pull this wall out a couple inches.) When I do that, I expect any attached walls to stay attached, but they don't.

Managing objects attached to each other is tricky for undo/redo operations or as soon as the user moves a bound object to a weird place. I don't think it will change soon.

Doors, windows, and room definitions also feel like they should stay attached to a wall when I move it, but they don't.

Use multiple selection (either with a selection rectangle or with shift key)

Included furniture: I'd like a car to be included to sanity-test garage dimensions. Also, shelf and rod closets [...]

The basic lists will never satisfy all needs. Feel free to download more models at Free models page.
The models search engine isn't perfect but playing with a few keywords or synonyms could help like radiator or heat. I add from time to time new keywords, but can't guess all of them, moreover since I'm French.

I had trouble with railings. Sure, you have them as a 3D model, but those don't define the edge of a room properly, you can't stretch them out to cover a long area without also making them look silly, you can't join them up to make corners properly, you can't make them arc, you can't join them to an existing wall, and so on. These feel to me like they should be a style of wall, not a 3D model.

3D models don't define additional shapes when you resize them, but for railings you can copy paste them and place them side by side with the menu item Furniture > Align side by side. You may also overlap a railing over the other one to get intermediate lengths.

I tried half-height walls (like a railing, but solid) by making walls that are 4' high, but those don't mix with room definitions that have a ceiling. As far as I can tell, there's no way to specify that a wall is important for a room definition, but the ceiling shouldn't touch it, and no way to have different logical and visual wall heights.

Even if I agree that ceiling management is quite touchy, you can manage its elevation by moving room points at the right location (see help about rooms for more information). You could also create a dummy higher level because Sweet Home 3D attempts to compute sloping ceilings only at the last level.

When joining walls of different heights, the join occurs at a 45 degree angle, which is never what I want.

Don't join them!

There doesn't appear to be a way to delete a room definition corner?

Right click to access to Delete point from room menu item (or create a new one where you right clicked).

0-height walls aren't possible. These are nice for outlining a room, but I'm stuck with 1" walls.

Programs don't like 0 too much [;)] More seriously, the smallest value you can enter is ⅛" not 1".

Sliding Doors don't embed themselves in walls the same way regular doors do?

These are doors for closets, probably named incorrectly but note that they are not in the Doors and windows category.

Stairs exist as a 3D model, which prevents customization. [...] No roofs

These are complicated options with a wide diversity of models. Looking in the forum could help you get ideas.

Also, stairs display on the floorplan as a featureless brown rectangle, not noting the direction they go.

You could draw some polylines as explained in this tip.

Maybe add an "Apply" button to the properties window to allow for easier playing around?

Yes maybe...

Cabinets tend to end up slightly misaligned. I put down some cabinets in a peninsula, and those things did NOT join up evenly.

Use the various Align items in the Furniture menu.

I should be able to assemble a kitchen that looks good without needing to manually enter in locations and do math.

Magnetism helps to place cabinets along walls beside each other. But you have to pay attention not to move your mouse too fast.