I would estimate than not less than 25% of my MP3 files do not convert to iTunes. I’ll take your word that Apple offers a variety tools that might overcome the problem, but why do I have to spend the effort digging them out and using them? Why doesn’t Apple just allow MP3s to load onto their players? Sony and everyone else does. Why require iTunes at all? It isn’t that iTunes is a more audiophile format, it’s only because Apple want to make it easier to get you music from iTunes, and harder to get from elsewhere. That theme seems common to all Apple products.
If your file were standard MP3, they'd play. It's obvious they're not. Apple fully supports the files I listed. I don't know what those files are, but it's obvious they're encumbered by their sellers with a proprietary Non-standard DRM. Nothing needs to be "converted" to any iTunes file type to play. They just play. You can convert them if you chose from one type to another within iTunes, but it is not required. You cannot increase bit rates, though, or increase quality, if it's not there to begin with.
If your files were obtained from RealNetworks, for example, they may claim they are MP3, but they might be protected with either HELIX or Harmony DRM schemes that would require a RealNetwork player/file decoder to play. If they were purchased from the Microsoft Zune store they used MS's proprietary DRM and require a Windows player to decode or strip them of the DRM. This means they are not pure MP3 files. If you got these files back from a commercial source before mid 2009, they most likely DO have DRM.
Apple has negotiated a way to handle all of these with the labels. . . Join a special service through iTunes and ALL your music from whatever source, however you got it, even pirated, becomes legally licensed, and you can download a DRM free version, at the highest bit rate free from iTunes to replace your low bit rate MP3s. I believe that service is $25 to get all your music legal and unDRMed in the best format available.