None of those are necessarily the case, assuming this mini-nuke is real and the descriptors of it are anywhere near reality.
1. It is impossible to talk about cost effectiveness if we cannot compare like for like. This mini-nuke (if it's real) will ultimately still be much slower than a proper nuclear submarine (even if it is faster than a traditional SSK), as well as displace much less and have less capable sensors, less volume for insulation and weapons and crew habitation facilities. In other words, you cannot compare cost effectiveness between two very different platforms.
2. We have no idea whether this supposed mini-nuke will be more stealthy than a proper nuclear submarine under similar operational demands/speeds/other characteristics.
3. We don't know how many mini-nukes will be procured versus how many proper nuclear submarines will be procured.
In other words, all three of these points are doubtful at best.
Instead of viewing the "mini-nuke" as being able to do the roles of a proper nuclear attack submarine "but smaller, more cost effective, and better in every way," you should probably view the "mini-nuke" as a "SSK but with longer endurance".