When one takes into account the fact that it is quite a bit more challenging to run the entirety of a street (e.g. East 39th St in Indianapolis) if it is in discontiguous segments, it maybe doesn’t seem quite so absurd that it be counted as different streets. 
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I’ve gotten used to the fact that I’m walking unique street names and I kinda like it. And that’s from someone walking what I think is the largest CS city, settled by Anglos with very unimaginative (ie repetitive) street names.
Yeah it is pain with say High Street, Church Road, Station Road etc etc. Just thought in the UK each “street” is given a USRN https://www.findmystreet.co.uk/ They tend to split up really long roads though into places so one long one near me say Portsmouth Road I see might have a Cobham, Esher, Thames Ditton “street” version of it but all in “Elmbridge” which is my home CS city. It is far worse in London of course with the all nested cities as still have to do a Station Road in every single nested city to count just one street.
On the roundabout naming piece, here’s the preferred mapping as it related to names. Tag:junction=roundabout - OpenStreetMap Wiki
Name tag: Only if the roundabout itself has a name, the
name=*key is applied (such as John’s Junction). It should not use the name of a road it connects. If the roundabout does not have an individual name, thename=*tag is not used.
So I imagine that would still cause issues with your solution.
Around the Minneapolis area (particularly in the northwest suburbs), there is a similar tendency to the Indianapolis example to keep street names the same along the same latitude or longitude, even if there is no direct connection. I could see the street counts in those cities skyrocketing as well. Not sure I have an opinion one way or the other yet 
example: Ranier Lane North - CityStrides
The roundabout naming thing is rough, but I suppose it’s a clean way of handling several differently named streets joining at a roundabout - leave it nameless rather than split it into several ways named for each street.
This “split on unjoined ways” idea definitely doesn’t seem to be holding up. I just skipped running some W 60s streets in NYC because of them being split up.
If I continue with this, I’ll definitely also need to include a distance factor … something sizable, probably on the scale of miles …
I’m used to the existing approach, but I understand why one might want to consider each section as a distinct street. I don’t have a strong opinion either way, but I do lean towards keeping things as-is. No big deal either way. That being said, there are several of these types streets in my town, and I find them to be odd.
I live in Columbus, Indiana, and while it’s much smaller than Indianapolis, it has several streets with more than one section. Many of the numbered streets are like this. Some of it makes sense if you know that there were once 2 separate cities, until East Columbus was annexed by Columbus in 1949. From what I understand, they attempted to eliminate the duplicate names for the non-numbered streets during the merger. For example one of the Maple Streets became Mapleton Street. But I know of one street that was skipped (Maybe the residents complained?).
- 26th Street has 4 sections. I think the 2 eastern-most sections were created after the annexation but they still decided to use this naming convention for whatever reason.
- 31st Street is another strange example. I think this entire street was created post annexation and they still created 3 sections with this name!
- And for some reason, they didn’t rename either Cherry Street as part of the annexation. So now there are 2 unrelated streets with this name. There’s also a North Cherry Street and a South Cherry Street, both immediately south of one of these sections.
And in larger cities there are many streets that were disconnected by the Interstate Highway System. In Cincinnati, I know this happened to Colerain Avenue. And Harrison Avenue has 2 sections, but this might predate the creation of I-75. Most people in Cincinnati are probably not even aware of the smaller sections unless they commute or live near them. And each section is in a different neighborhood, so it I guess it kind of makes sense to consider each a separate street.