"Inside Your Heaven" was only included on the North American album release of SH, as a 14th bonus track. It doesn't appear on the album as sold in the UK (and I'd assume not on most other international releases). It stemmed from American Idol (and Bo Bice also released a version) rather than from the planning for the album as a new creative work
The album track "Some Hearts" represents the "Pop half" of that album, which Carrie has explained by saying that they had to carry the expectations of a large mixed audience from AI, and introduce them gently to the Country format. It was released to some Pop formats in roughly the same time frame as JTTW, probably as an insurance policy. It didn't chart as highly as JTTW, and the need for that approach passed. From what she's said (basically, that she doesn't mind if tracks are picked up by other formats, but she won't deliberately target them). I don't see Carrie as having wanted to promote in that way in any of the later eras. People often ask "Why don't they release track x to format y ...?" - as if not doing so is some kind of oversight or weakness by Sony Nashville. But, so far, it seems to have been Carrie's preference - her label is not likely to release something she won't promote.
As for the thorny issue of why there are usually only four singles - I would also like to see more. But I think the issue probably revolves around reluctance to risk her record of always getting singles into the top couple of airplay places. Although almost any Carrie track would be likely to do well, some of the fan favourites would probably be considered more risky for reaching the very top of the airplay chart . And it's likely that diminishing returns would be expected from radio, if there'd already been four in succession - as set against the fresh build up of anticipation after taking a break for the next album.
I do think this high chart priority exists as part of the label's view of Carrie's role as a commercial leader, and it also seems to be important to many fans, but I don't know how important it might be for Carrie personally. However, I think if it was modified, there'd be both a greater chance of one or two more singles being released, and also a greater willingness to risk some of the deeper album tracks.