In addition to Windows simply not having support for Linux file systems, Microsoft cannot reasonably take on the responsibility of guaranteeing your data will be safe if they try to support them. For example (and completely hypothetical), say the ext4 team improves performance by recognizing a new ext4 inode format that is not backward compatible. Windows next modifies your data but mixes the old format with the new one, because it doesn't know about the change, and corrupts your data. Who will you blame?
For years, as my memory recalls, the Linux kernel had read-only support for NTFS, and write support was labeled UNSUPPORTED for years after it was introduced. The Linux kernel was obviously very concerned about data integrity until they were confident their NTFS file system support was fully stable and understood. Now imagine how much harder it would be on the kernel team if Windows had 3-5 other filesystems just as popular as NTFS. (Think: ext3-4, XFS, ReiserFS, Btrfs, etc.)
diskmgmt.msc. The only thing here is that you're asking Windows to understand a filesystem it does not know about, just like you could be asking it to use a device (e.g. a modem) it does not know about.