Because the key `old_name` does not apply to the sidewalk. If I had tagged the sidewalk as `old_name=Brandywine Way`, that would've meant that the sidewalk itself used to be named "Brandywine Way," which is incorrect. `street:old_name` perfectly encapsulates the situation I am accounting for here, where 𝘁𝗵𝗲 𝘀𝘁𝗿𝗲𝗲𝘁 𝙖𝙨𝙨𝙤𝙘𝙞𝙖𝙩𝙚𝙙 𝘄𝗶𝘁𝗵 𝘁𝗵𝗲 𝘀𝗶𝗱𝗲𝘄𝗮𝗹𝗸 used to be called Brandywine Way.

If you run the validator in JOSM, it will complain that there's an "alt_name without name." If the name "2100 South Freeway" isn't signed anywhere, that can be indicated with `name:signed=no`. If there is no other name that the freeway goes by, wouldn't the nickname that locals use (which is the only name aside from the designation, which is not a name) be put in `name` (since there's no "official" name)?

Is it? Wikipedia says, "However, an eastbound traveler wanting to continue on the surface portion of SR-201 to State Street must exit on 900 West, head north briefly and then turn eastbound on 2100 South; a westbound traveler on 2100 South wishing to connect to the freeway must take an on-ramp from the surface street just before 900 West. [...] Now on the four-lane 2100 South, [...]" To me, this sounds like a continuation of SR 201, but maybe I misinterpreted what it said.

According to Wikipedia, yes it does, apparently, despite clearly not being built to Interstate standards (no physical barrier between the carriageways).

I explained this in detail on a previous changeset involving these ways. Long story short, the name of the associated street was Brandywine Way, but this segment is no longer in use, despite being completely intact otherwise.

1. This specific road section, the one I changed just now, does, in fact, have no traffic lights, qualifying it as fully controlled-access highway.
2. osm.wiki/Proposal:Motorway_classifications

...which is why I tagged it as highway:motorway=primary...

This is only an incomplete interchange. There is no way for southbound drivers to enter I-215 unless they also go to 3900 South. Similarly, northbound drivers on Wasatch Blvd have no direct access to the freeway anymore, unless they again turn onto 3900 South.

For the hundredth time, highway=motorway does NOT indicate a road's importance in the network! Quoting Joseph RP from earlier, "the freeway section of the 93 Business loop is only tagged [as] a motorway for its physical characteristic rather than its importance, and would be a primary road itself if it weren't built up to freeway standards between I 11 and VM [Veterans Memorial] Drive." That's why I tagged with highway:motorway=primary. If you really wanted to, you could ditch highway=motorway entirely and replace it with motorway=yes (and highway=primary), but I don't recommend doing this until the community reaches a consensus (Spoiler alert: it hasn't—yet).

highway=motorway does NOT indicate a road's role in the network. Rather, it's applied based on physical characteristics. All of these roads (plus Rancho Drive between Rainbow Blvd and Ann Rd, for some reason, according to Wikipedia) are controlled-access highways: There are no at-grade intersections or pedestrian crossings (except at the very end), and the speed limit is high (~60 mph), so all of these would be tagged as highway=motorway.

Okay, I just looked at them, and I guess that makes sense. But what should be done about the routing mistakes ("turn right" onto Boulder City Parkway)?

...which is why I reverted this changeset (along with a few others)

Reverted changesets 173472314, 173479852, 173501716, 173502305, 173502568, 173503941, and 173504156

Still broke roads

changeset/173504156

I simply downloaded the Las Vegas relation using JOSM's "Download object" function. Per OSM's "Keep the history" rule, I used Ctrl + Shift + G to replace the old boundaries with the new ones, while preserving the history. (Maybe I'll disconnect the boundaries from the roads first.)

Neither of your scenarios are the case here. The road segment still exists, even if basically no one uses it anymore. Older maps of this area showed that Brandywine Way was connected to Lorenzi Street via this highway segment. However, the former's western terminus was moved from the latter to a cul-de-sac (dead end), where it remains today.
As mentioned before, the statement "The street does not exist anymore" is false; therefore, any other statements dependant on this one are irrelevant. Carto doesn't render it (presumably because it's tagged with `disused:highway`=*), but if you go to this location on any map service that provides satellite imagery, you too will see that the road still exists.
Also, there's this expression used in OSM: "Any tags you like."

Hello, please do not change "street:old_name" to "old_name." street:name refers to the name of an associated street of, say, a sidewalk. According to old maps of the area, the associated street was part of Brandywine Way. However, you tagged the footpath as "old_name=Brandywine Way," which is incorrect. See osm.wiki/key:street:name for more information.
So, then, with the street itself being tagged as "old_name=Brandywine Way," a natural extension/interpolation would be to tag the surrounding footpath as "street:old_name." Thanks!

changeset/173459509

Hello, why did you create a tertiary road (Discovery Bluff) that doesn't link to any tertiary (or higher) roads?

I also used the website provided. Basically, this node with barely any tags attached to it was moved to its proper location, so I added an address. I used Google Maps for those two, but I used the website (which is uh, interesting to say the least) for everything else.

I looked at it more closely using Bing Maps, and I couldn't find one. As a result, I removed the tag entirely.